That's kinda two different questions.
1: when do we think he's ready
2: when do we think the team will use him.
Possibly a third as well
3: When would he be a starter?
No one is going to maintain the numbers Anderson had in his AA tenure last year indefinitely, but if he puts up good numbers in Portland he might ready to be be promoted to Pawtucket in the second half. Sort of like Ellsbury and Lowrie two years ago. Or he could spend all year in Portland depending on what Bailey, Carter, Natale and McAnulty do with the 1B, backup 1B, DH and LF spots. Anderson is very young and he's not on the 40-man, and we have players under contract for all the significant positions he can play until 2011. There's time.
In all likelihood if Anderson is promoted midseason it'd be Bailey who was the roster casualty. IIRC he's out of options and is just too old to hold onto if Anderson starts seriously beateing the door down. Natale could go too, since he doesn't have the range for 2B or the power for 1B, but seriously the guy is an OBP monster, is still young enough to have a bit of projectability, and I suspect the team will wind up wanting to hold onto him as bench fodder. Guys who can put up a .400 OBP consistently throughout an otherwise up and down minor league career aren't guys you let go of in a hurry.
Once he's in AAA it's just a question of a spot opening up. In order to gain big league playing time Anderson will have to earn his way past Bailey, Carter, and McAnulty for any cups of coffee going around as a result of possible injuries to Lowell, Papi or Youkilis. He also has Bates and Still trying to run up his back for 1B/DH time in Portland, which is not high odds for either prospect but is something to think about.
Given the depth ahead of him it's not a given that he even makes the September roster. If we want a 1B there, I'd have to say both Carter and McAnulty need chances more than Anderson does, and IIRC Lars is not on the 40-man roster yet.
It would depend on a few things falling his way that may not. In all likelihood we're looking at a strong possibility of a 2010 debut and a much smaller possibility of a debut this year.
Now if we're talking purely on the basis of his talent alone and roster calculus doesn't enter into it, he could probably do all right in the big leagues right now -- and indeed there are teams out there that would have pushed a guy performing as Anderson did in the low minors much harder and he'd probably be in the big leagues right now. An example of this kind of thinking is Billy Butler. But since the decision to rush Butler really didn't do him any favors I don't see where there's much to lose by giving the kid more reps.
By 2011 assuming nothing goes wrong I'd like our corner IF to be Youk at 3B, Anderson at 1B and Natale as the backup 1B (a position where I think his exceedingly strong plate discipline can compensate for his relative lack of pop and make him a fine pinch-hitter and righthanded backup to the lefthanded Anderson).