Not according to this --
http://marvel.com/universe/Bullseye. It says he joins the Avengers under the guise of Hawkeye, but is eventually outed... so at least not in most of the Marvel universes. Plus, his name is apparently Lester while as far as I know most incarnations of Hawkeye are Clint Barton. With that said -- I think it's possible that one of the wolves is Bullseye. I don't think it's likely that Hawkeye autoconverted into Bullseye.
*disclaimer -- most of my information comes from googling things. So feel free to correct me, people with more comic knowledge.