They can tell America whatever they want but they’d be wasting time they could be spending trying get out of major population centers, as the counter strike would already be en route.
What would be more debatable (and scary as you know planners on both sides have seriously considered what to do in this situation, and a plan is already in place) is what happens if Russia nukes Kyiv (or somewhere else in the Ukraine). Its not super likely, but its also not a completely crazy and out there outcome, especially if things continue to go south for Russia to the point Putin’s position is become dicey.