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TL;DR: No.

People often reject Ayn Rand's ideas, uncritically and wholesale, for her alleged hypocrisy in accepting social security. They do this even when you point out the irrelevance (see here and here), and even though the hypocrisy itself, if real, wouldn't refute her ideas, only her integrity.

This article by Open Culture, for example, accuses Rand of said hypocrisy. It also links to an article by Onkar Ghate on the Ayn Rand Institute's website that was supposed to clear up the confusion. Rather than address Ghate's arguments, Open Culture lazily dismisses them as "convoluted".

Both articles could be better (but make no mistake, the one by Open Culture is much worse). So here's my attempt.

Rand collected social security toward the end of her life because of lung cancer. Not only were her actions consistent with her philosophy, and not only did she argue for this consistency in print – as Ghate points out on both counts – but, I should add, she did so a decade before collecting social security (as opposed to, say, coming up with an excuse after the fact).

Open Culture’s opening paragraph reads:

A robust social safety net can benefit both the individuals in a society and the society itself. Free of the fear of total impoverishment and able to meet their basic needs, people have a better opportunity to pursue long-term goals, to invent, create, and innovate.

Let's be clear about the nature of this "social safety net". Some people are taxed, against their will, to have their wealth partially redistributed to others 'in need'. In other words, bureaucrats steal money from the rich and give it to the poor, Robin Hood style. There is no way to opt out; even those who are happy to pay taxes cannot be said to consent.

So the question arises: if a "robust social safety net" is such a good idea, why must it be hoisted on everyone by force? Why don't people cooperate voluntarily to create such a safety net?

The article relies on the mistaken notion that social welfare is the political realization of genuine good will among the people. In fact, the opposite is the case. As Rand explains in her essay 'The Question of Scholarships' (from which Ghate also quotes, albeit without giving a source):

It is altruism that has corrupted and perverted human benevolence by regarding the giver as an object of immolation and the receiver as a helplessly miserable object of pity who holds a mortgage on the lives of others—a doctrine which is extremely offensive to both parties, leaving men no choice but the roles of sacrificial victim or moral cannibal. A man of self-esteem can neither offer help nor accept it on such terms.

Conversely, Rand was not opposed to genuine help. She writes:

It is morally proper to accept help, when it is offered not as a moral duty, but as an act of good will and generosity, when the giver can afford it (i.e., when it does not involve self-sacrifice on his part), and when it is offered in response to the receiver’s virtues, not in response to his flaws, weaknesses, or moral failures, and not on the ground of his need as such.

Skipping some, the Open Culture article continues:

[T]here are some, including the acolytes of Ayn Rand, who believe as Rand did: that those who rely on social systems are—to use her ugly term—“parasites,” and those who amass large amounts of private wealth are heroic supermen.

More nuance is required here. Rand did not think that everyone who relies on social systems is a parasite, nor did she think that everyone who is wealthy is heroic (she disliked crony capitalism).

In the referenced essay, Rand differentiates clearly and precisely between legitimate and illegitimate recipients of 'public' money:

The recipient of a public scholarship is morally justified only so long as he regards it as restitution and opposes all forms of welfare statism. Those who advocate public scholarships have no right to them; those who oppose them have. If this sounds like a paradox, the fault lies in the moral contradictions of welfare statism, not in its victims.
[...] Whenever the welfare-state laws offer them some small restitution, the victims should take it.

And, a bit further down, contrary to Open Culture’s rose-colored account of people having "better opportunity to pursue long-term goals, to invent, create, and innovate":

[T]the anti-collectivists are innocent victims who face an impossible situation: it is welfare statism that has almost destroyed the possibility of working one’s way through college. It was difficult but possible some decades ago; today, it has become a process of close-to-inhuman torture. There are virtually no part-time jobs that pay enough to support oneself while going to school; the alternative is to hold a full-time job and to attend classes at night—which takes eight years of unrelenting twelve-to-sixteen-hour days, for a four-year college course. If those responsible for such conditions offer the victim a scholarship, his right to take it is incontestable—and it is too pitifully small an amount even to register on the scales of justice, when one considers all the other, the nonmaterial, nonamendable injuries he has suffered.

Observe also that things have gotten even worse since; that college graduates often owe tens if not hundreds of thousands of dollars in student loans.

You may say that Rand is only addressing the issue of accepting publicly funded scholarships in particular. But she broadens the context to apply to all kinds of ‘public’ money (bold emphasis mine):

The same moral principles and considerations apply to the issue of accepting social security, unemployment insurance, or other payments of that kind. It is obvious, in such cases, that a man receives his own money which was taken from him by force, directly and specifically, without his consent, against his own choice. Those who advocated such laws are morally guilty, since they assumed the “right” to force employers and unwilling coworkers. But the victims, who opposed such laws, have a clear right to any refund of their own money—and they would not advance the cause of freedom if they left their money, unclaimed, for the benefit of the welfare-state administration.

Rand wrote this in 1966 – again, well before ever collecting any social security, and presumably before having reason to think she would ever need it herself.

Open Culture alleges that Rand failed to realize that "none of us is anything more than human, subject to the same kinds of cruel twists of fate, the same existential uncertainty, the same illness and disease" – and then points out (in a possibly celebratory way) that Rand herself became the victim of such misfortune due to her lung cancer. Of course, Rand was well aware of the fact that misfortune may befall any of us – who doesn't know that? – she just didn't want one person's misfortune to be a claim on another's life and property, as Ghate points out. She instead wanted a society where the answer to poverty is the freedom to achieve – a freedom which, in today's America, is being systematically violated.

The Open Culture article quotes Rand's assigned social worker, Evva Pryor, as saying that Rand hesitated to accept social security. But then Pryor partially invokes Rand's own argument: that she had a right to such payments.

If anything, Rand's hesitation to collect social security might, by uncharitable eyes, be considered hypocritical. But the fact that Pryor believes to be arguing against Rand while really invoking Rand's argument is evidence that Pryor did not understand her. So I advise against accepting Pryor's account uncritically.

Toward the end of their article, Open Culture grossly misrepresent Rand's stance by claiming that "the sole function of her thought is to justify wealth, explain away poverty, and normalize the sort of Hobbesian war of all against all Rand saw as a societal ideal." Not only does this minimize Rand's contributions, it's also false: Rand advanced "the Objectivist principle that 'there are no conflicts of interests among rational men.'" (See The Virtue of Selfishness, chapter 4 'The "Conflicts" of Men's Interests'.) Open Culture, on the other hand, is in favor of a society where those in need may loot the wealthy – so who's advocating a "war of all against all"?

But I suspect it doesn't matter much what Rand did – her detractors would find a way to smear her regardless, and the welfare state produces otherwise unnecessary conflicts between and within people anyway. As she writes herself:

It is a hard problem, and there are many situations so ambiguous and so complex that no one can determine what is the right course of action. That is one of the evils of welfare statism: its fundamental irrationality and immorality force men into contradictions where no course of action is right.

In conclusion, Rand was not a hypocrite for accepting social-security payments. On the contrary, her philosophy stated well in advance that she had a right to such payments because 1) she opposed the welfare state and 2) she regarded these payments as restitution.

You may disagree with her ideas, but the hypocrisy charge does not stand up to scrutiny.