YES.
I assigned her to a different location once by accident, and I feel the exact same way ever since. *I* was the guy who told her to stick with family no matter what, ironically...
For that same reason, I always pay attention never to dismiss Nick to any place but his agency. It's a different story with companions like Dogmeat, Strong, Curie or even Cait; who want to leave or can no longer stay at their original location, but Piper and Nick are (in an ultimately imaginary way) important citizens with obligations in Diamond City.
That's actually a good idea; I could just buy the two a new house. Not like I'm spending any of those caps on anything, anyways.
Brother, that's a major spoiler. Please edit it out.