Right now: Maybe.
The thing about this is I know from Cast & Crew they’ve been let go. So it’s just like REAPER. If they renew the show they have to go back and get cast & crew to do new contracts. That isn’t easy. In the case of REAPER it’s what stalled the show, one (possibly two) told Mark Gordon Productions they weren’t interested unless they could be assured the quality was there in the writing.
What MY NAME IS EARL has going for it: It’s a 13 episode order that will push it over 100 episodes and enter it into the blessed land of syndication. So that means a lot of money for the cast. They’ll make the deal. It also has the show’s creator still on board (something REAPER doesn’t).
It’s early talks and it could go either way, however it shouldn’t have any issues getting the cast and crew to sign up for one last run (or possibly more). TBS will likely want some kind of multiple season offer (so if it works for them, it keeps going).