Influenced them? Absolutely. Supporting them? Mmmmm, maybe, maybe not. Hard to tell on that point. See, most of what we know about Socrates' relationship with the Thirty comes through Plato, who's at pains to distance Socrates from the Thirty, Critias in particular. As with so much in Platonic dialogues it's hard to tell where Plato ends and Socrates begins. The Thirty and other oligarchs were quite intimately associated with Socrates' circle. Critias was, of course, one of Socrates' students, but according to Diogenes Laertius Plato was actually Critias' nephew, which is a spoopy thought. Alcibiades, too, was of course a member of Socrates' circle and had aided the oligarchic coup in 411--being in the constant company of aristocrats Socrates would've found it rather difficult to stay away from opponents of the democracy, and several of Plato's dialogues seem to suggest that Socrates himself wasn't necessarily a big fan of the democracy, although again it's hard to separate Plato from Socrates. We do know a few things about Socrates' dealings with the Thirty. That he knew them during their time in power is certain, as is apparently the fact that the Thirty thought they could trust him. In the Apology Plato says that the Thirty brought him and four other guys whose identities are not given into a council and told them to go arrest Leon of Salamis, whom Xenophon tells us was unjustly executed later. Socrates, instead of obeying their orders, just decided to go home while the others went to Salamis to fetch Leon. Now, Socrates' disobedience aside, we're faced with the fact that Socrates did get called on by the Thirty--what are we to make of that? Socrates says that he was hardly the only person whom the Thirty called on to do their dirty work, that--much like the Sullan proscriptions--the Thirty enlisted as many people as possible, apparently (so Plato claims) to spread the guilt of their injustice. Whether that's strictly true or not, we're still presented with a second problem, this one quite damning. Socrates, a man apparently of decent means, stayed in the city during the rule of the Thirty. When the Thirty came to power the democrats of the city, those that had the means to up and move, all went into voluntary exile--those who remained were those who couldn't afford to leave and those who supported the oligarchy. The charge of remaining in the city was a serious accusation, even if Socrates could not be prosecuted for it. Though Socrates makes excuses for himself in the Apology they're not terribly convincing, and his presence in the city would have been something many people would have found very suspicious and unsettling.

I should mention that the charge of corrupting the youth is not actually a charge of influencing the Thirty. Socrates could not legally be charged of any crime involving the Thirty, because after the democracy was restored a general amnesty was put into effect, where the democrats decided to basically pretend that the Thirty had never happened, since so many people had been roped into their schemes. Of course at the same time Socrates was in a sense being put on trial, at least in part, for his associations with the Thirty, but the charge against him did not directly involve the Thirty or Alcibiades (whom Plato at least points to as one example of a youth who ended up corrupted, despite Socrates' good influence). The charge against Socrates was multifold, with all the parts connected: he was charged with not believing in the gods (the Greek actually means "naming" the gods, but the idiom is something like "acknowledging"), teaching others to not believe in the gods, and then teaching them to believe in new gods. Socrates points out in the Apology that the charge of not believing in gods but spreading the belief of new gods is absurd, since he can't believe in gods and not believe in gods simultaneously, but against the charge of corrupting the youth, which is associated with those charges, there's not actually much of a defense he can make besides asking the fathers of his pupils what they think. The idea is that Socrates had pissed off and humiliated a lot of very important people, so plenty of people were upset already, and he was, as one of my professors put it "asking a lot of questions that many people thought he shouldn't be asking." Worse yet, Socrates rarely answered those questions, but left the young aristocrats who flocked to him searching for answers, left intentionally without much guidance--that was part of the point of what Socrates was trying to do. Some of these youths, like Alcibiades or Critias, ended up with bad answers, and a lot of the rest were confusing themselves and other people, often to the humiliation of their elders. And the questions that they were stumping themselves and other people with were very uncomfortable: what is truth, reality, religion, etc.? Add this to the rather suspicious activity of Socrates' association with the Thirty and other supporters of the oligarchy, as well as his very questionable decision to remain in the city during their rule, and to a lot of people it must have seemed like something fishy was afoot, whether Socrates ever did support the Thirty and oligarchy (a point which Plato stresses was untrue)