Not always. Nirvana used to hate being associated with a lot of their "new" fanbase when Nevermind got popular because as teenagers they were made fun of and beaten up by jocks, and now all of a sudden, jocks were showing up at their shows and Cobain hated it.
Also, the same can be said for Queens of the Stone Age. Josh (lead singer) continually gets angered by fans in the audience being jerks and makes fun of them.
Ie:
http://www.nme.com/news/queens-of-the-stone-age/37399
I don't think a band always has the fan-base it has or wants. It's music, it's just the way it works.