No, he didn't have a role in the collapse of the Soviet Union. At this time he was working with Anatoly Sobchak who was a mayor of Saint-Petersbourg. So, you could say he was relatively important in Saint-Petersbourg but not country-level important at all.

If by "a coup against the government of the USSR" you mean GKCHP (ГКЧП), I think it'd be oversimplification to say that this event was organized by KGB. One of them truly was the head of KGB) but still, it didn't look like organized attempt at anything at that time and doesn't look like organized attempt at anything now. Anyway, Putin's boss, Anatoly Sobchak, didn't think he had to do what GKCHP wanted and Putin immediately quit KGB.

All of this happened 8 years before the beginning of Putin's presidency.

In 1996 Sobchak lost another round of elections, so Putin lost his job. After that he came to Moscow, where he was invited to work in Yeltsin's administration. Two years later he became a head of FSB (KGB successor). Three years later (1999) he became a prime minister.

It seems that the main role in his promotion was played by Valentin Yumashev, Yeltsin's son-in-law. Yeltsin and his closest associates were worried that after Yeltsin all the progress on the way to democracy would be lost. And maybe they were worried about their future fates also. Yeltsin as a politician wasn't in a good shape, he almost lost his own President elections in 1996 (and some says that he really lost it, but it's quite hard to say if it's true or not). Anyway, all these years there was a fear of communists' comeback, so Yeltsin's associates (sometimes this group of people is called Family, Семья) wanted to have a good successor. The one who wasn't communist, the one who owes them a lot, the one who wouldn't betray them. They wanted guarantees.

Putin at that time seemed for them as a good choice. He believed in democracy, he had his own code of honor, he was loyal to them. And he really owed them a lot. So, he was chosen not because he was an influential politic with a lot of connections or was a rich guy with a lot of money and power. He was chosen because he wasn't. For people he was a relatively unknown. He had worked just several months as a Prime minister, and before that he was a head of FSB (not a really TV celeb), and before that he was an official in Yeltsin's administration (not a really TV celeb also).

So, the question is: did it work for the Family? Yes, it mostly did. You can say a lot of bad things about Putin, but he is obviously loyal to those who is loyal to him. Valentin Yumashev is still his advisor. Roman Abramovich is still a billionaire and so on.

Some people who helped Putin on his way to presidency fell out of his favor though. The most prominent example is Boris Berezovsky, who wanted to control Putin right after the elections. It didn't work out for him. In 2006 he ran to London, after that he gradually lost a significant part (maybe, most) of his assets, and in 2013 he was found dead at his London house (suicide). But even Putin's critics won't say Putin betrayed Berezovsky. If there was a betrayal, it was the other way around, and after that there was a revenge.

Did it work for democracy? You know it didn't.

But, actually, during the first 8 years, it was quite okay although Putin tried to control the media right after he became a President and there was a quite strange and tragic story with Russian billionaire Mikhail Khodorkowsky. But democracy and freedom of speech didn't just disappear in one day, it was a slow and painful process.

Obviously, Putin's experience in secret service have some influence on his strategy and decisions, but I don't believe it was his plan from the beginning. He was very lucky because before him Russians were very poor, and during his first eight years they became much more richer and happy. If he quit, he'd be remembered as one of the best Russian rulers of all time (despite some of his mistakes and shortcomings). But he didn't quit, and he'd changed.

If you want to read more about this, I can recommend an excellent All the Kremlin's Men: Inside the Court of Vladimir Putin by Mikhail Zygar. Also, Berezovsky's time by Peter Aven (not sure if there is an english translation). But please bear in mind that this is still quite modern history for Russia, some parts of this history are literally dangerous to touch, a lot of people who could tell us something prefer to keep their silence, so there is a lot of gaps, and misunderstandings, and mistakes, and downright lies in all the books about that.