No, Putin's hold on power has become precarious of late, even if he gave the order to use a nuke (a low yield would be the size of a Hiroshima bomb) it is the military commanders who would actually initiate the strike and I doubt that they would do so, they better than anyone would know the consequences for themselves and their families. This isn't a scenario where hundreds of american missiles heading for Russia have been detected on radar and a well oiled machine is set in motion to counter strike, a commander would be told from a failing dictator to send a nuke to a country on the border with Russia for no rational purpose. It would be Putin's last order.