Of course not. But if they close the border to all, they would be part of all.
There are plenty of reasons for Americans to leave regardless.
Putin because he has been humiliated by Ukraine can't be seen to admit that the country that he has trashed as inferior for so long did that to him. So he's blaming Nato, the West, and especially the U.S. If Putin escalates in some way that goes beyond the Ukraine and/or Nato responds to escalated atrocities like nuclear, chemical, attack a target in a Nato country, etc. who in their right mind would want to be an American there then, enemy number one?