Question...If I have Deadpool attached to either the Avengers or X-Men team base, would I still be able to attach/swap a word balloon to him on my turn and it would affect the entire base?

No and no. The dial is what houses the power that makes word bubbles mean anything, along with allowing you to attach/swap them, and when a guy's on a team base, his dial's out of play. So those effects would not be accessible or having any effect.

That said, the word bubble, if attached to Deadpool while he's NOT on the base, would continue to be on the figure while he's on the base [I assume, 'cause why not?], but it wouldn't do anything.

No. Not unless a game effect specifically allows that.