It's certainly possible. Just getting out of Dodgers Stadium would likely add ~50-60 points to his OPS. Then factor in that he's more or less a dead-pull righty and you could argue even a bit more improvement into that playing half his games at Fenway.
The question is all about health and defense, neither of which I'm really qualified to assess.
Both Fangraphs and B-Ref absolutely hate his defense over the last few years, and while I don't have access to the Fielding Bible, the link below suggests John Dewan isn't so keen on his fielding chops either:
http://www.fieldingbible.com/kemp.asp
Maybe you get comfortable that he can live in left at Fenway and not be a liability, but to do that he's going to have to post a wRC+ in the 125 or better range, he's going to have to stop getting caught stealing on the basepaths 50% of the time, and he'll have to play 130+ games a year. It just seems like far too many things have to go right simultaneously for it to make sense without LAD heavily subsidizing him. They'd need to throw in something like $40M to entice me; has a team ever thrown in remotely that much? Even then, you've still got Kemp on the books for 5/$68M after this season, no small investment.
EDIT - clarification