Preston has not annoyed me yet in my game which is probably up to 110 hours by now.
I haven't really paid much attention to him in the 1st place. I rescued him and the others, set them up at Sanctuary and basically ignored for the most part. I've been using Dogmeat and then Codsworth to do some exploring and also resource grinding since I wanted to have a good stockpile of crap before actually trying to build up a settlement beyond just placing water pumps and turrets.
I don't think I bothered with the Tenpines minuteman quest until about 40 hours into the game and I did not start Outpost Zimonja until about 70 hour into the game. Outpost Zimonja is still an active quest since I have not bothered building the settler recruitment signal tower yet.
I have only been using Preston as a companion at about 85 hours into the game. I can't recall if he gave me any radiant quest to dispatch raiders or whatever. It's possible, but like I stated I have been ignoring through out most of the game. I only just got to Diamond City last night before turning off the game so I might switch him out for Piper over the weekend...