That is absolutely a possibility, but not a certainty, and a very dangerous gamble to make. That said, Europe probably does need its own nuclear deterrent and its own anti-ballistic missile defense.

They only need one working nuke out of their 6000. I'm sure at least one of them is operational.

If they only have one and they use it, they've effectively solved the Russia problem themselves.

But is that a game of Russian roulette you'd want to play?

No one wants to play that game. The Russians boast about the nuclear bombs, then suddenly goes quiet.

They were going to use them if Ukraine entered Russian soil!

Then they declared that parts of Ukraine was Russia. Ukraine took back some cities on supposedly "holy Russian soil" and nothing happened.

Then Ukraine took a chunk out of (actually) Russian Kursk. Suddenly no talk of nukes for a while.

What would they do with the nukes? Suicide?

The nukes are to help with the Second Coming of Jesus. No, really:

https://en.m.wikipedia.org/wiki/Nuclear_Orthodoxy

Even if not “operational” you could strap the warhead to a conventional bomb and really ruin a cities next few hundred years.