If the order were given
If the order came down from Putin to use a nuke, in any scenario, I think there's a good chance Putin would be removed from power. The military chain of command might obey the order, but they very well might not. The civilian leadership and various power centers in Russia would be horrified with such an escalation. Also, it would clearly be the desperate move of a militarily defeated leader, and that story doesn't play well in Russian history.