If he thinks that he can get away with it and clearly uses it in defense of his forces, yes he will do it. The interesting part with be what happens next. Article 5 of the NATO treaty that would involve the US and all of NATO is based on defense of a NATO ally, but if the NATO ally is the aggressor, I am not sure that it applies. So if he were to do so over Syrian territory, Article 5 would likely not be invoked, although Turkey would clearly be calling for it. The Russian Nuclear arsenal is THE linchpin in Putin’s power. He would gladly demonstrate his willingness to use it. Never underestimate the extreme levels a narcissist will go to prove his merit.
I don’t think Rusia will nuke Turkey itself. I do however believe they would wait for a sizable Turkish force to encroach in Syria and nuke the Turkish troops on Syrian land. That is a checkmate and a half.