They absolutely would get involved. You can't just light off nukes in Europe, because it poisons the whole continent. Strategic or tactical nuclear weapons usage (or even threatened usage) to annex border states requires a response or else you're going to be skipping straight to "full scale launch" when the aggressor asks for something you're not willing to give up.

Fortunately the bet in that regards is that Putin's own military and associates would depose him almost immediately - intentional nuclear weapons usage changes the calculus on a lot of things, since you're now into "you, your family and your country will definitely die if he stays in charge". The Russian people aren't behind this war.