Yes, you are right in identifying the logical absurdity of Putin using nuclear weapons to attempt to win the war, when in fact, nuclear will ensure his downfall.
But he wouldn't agree with the downfall conclusion, as he believes the premises will lead to victory.
Let's hope he is wrong, and even more so, that other premises arise beforehand that disrupt the nuclear threat.
However, I don't believe they will, and he'll use them in the near future.