Well, if Putin launches nukes first, then I reckon it's safeties off for NATO as well then...
The last I read, and not going to post the details in particular, but a country backed by the US has determined that they would have a ~80% success rate at neutralising a nuclear ballistic strike. 80% is rather low considering the weapon and its potential destruction, not to mention that neutralising a nuclear weapon would also carry consequences, pending where it is being neutralised. Considering that Russia has nuclear warheads by the thousands, and would desire to use the weapons, they would commit to multiple strikes to negate any possible neutralisation.
A nuclear launch won't be pretty, it can be assured that there would be an immediate nuclear response by the targeted alliance. From what is publicly known, I don't believe Russia could respond as well to nukes as the NATO and some other UN countries can. It is likely that Russia will come second, and second still being last should such circumstances arise.
Russians are intelligent, they know it is a last resort.