It's hard to guess exactly how long it will take him. That our OL is still trying to find itself makes his getting comfortable in the offense even harder.
The two guys he is most compared to, Jake Delhomme last year in Carolina and Matt Hasselbeck in Seattle, 2001, both had talented solid lines in front of them. Jake and Matt both had less experience as an NFL regular season QB than AJ does at similar points in time, and Jake caught on very quickly starting 15 games and having a QB rating of 80.6 . It took Matt a little longer, he started 12 games in '01 with a QB rating of 70.9. In his 2nd season, things picked up for him as his rating went up to a solid 87.8. Last season his stats were at least borderline Pro Bowl. I don't watch the Pro Bowl so I don't know if he went or not.
AJ is equally talented and more experienced than either of them were, but he would be possibly hindered by the lack of cohesion on the OL, unless they really come together quickly. If he does become the starter early in the season.