Absolutely not.
Even if Doc were to leave, I would not want Thibodeau as head coach. He's fantastic as associate head and I would hate to lose him there, but better to not have him at all than to have him as head coach.
In general, I think it's a bad idea to put a first time head coach in charge of a veteran team with periodic chemistry issues. To exacerbate the first-time problem, Thibs never played in the NBA. Most players to some extent and some players to a large extent will be thinking "he doesn't know what he's talking about, he hasn't played at this level." That sentiment is mitigated after a non-player coaches successfully for a while, but the time to build up that reputation is not on an aging contender. Thibs would be better off starting with a young, building team.
Don't forget that the one time he coached this year, he didn't make any substitutions. Not being able to adjust on the fly or react to an unexpected situation is a bad sign.
Finally, while groupthink is dangerous... I can't help but wonder why all the teams that have interviewed him in the past few years have chosen not to hire him despite the tons of credit he got for 08 championship.
If Doc decides to leave, I'd rather the Celtics brought in someone completely new (but experienced) to put in a different system and maybe move along the transition from the Pierce era to the Rondo era in the process.