USATF rules now allow (adult) athletes to join a club in any Association, but you generally can't count in team scored events like Club Nationals. Masters track nationals does have team scoring, but that meet is a joke, so I think you can represent whatever club there. (I don't know what the youth residency rules are, they don't matter for this discussion).
So the way the rules stand right now, a masters pole vaulter could join pretty much any track club and there wouldn't be much downside. You couldn't do it automatically though, you'd have to send out a few emails to get the transfer done.
Edit: let me add that if you rely on USATF liability insurance for practices you host or participate in, it would get more complicated.