Maybe they would have, but Bosh didn't even play until game 5 in that series. Once they got Bosh back to even like 80% (games 6 and 7) the C's had no real chance. Miami with Bosh was just such a vastly superior team to Boston at that point.
And frankly, Boston was only in that series because Rose blew out his knee. I don't think Boston gets by Chicago that year, but Rose blowing out his knee allowed 8th seeded Philly to win the 1st round. Boston had to go to 7 just to dispatch the Sixers after going 6 with the Hawks in the first round. That team was fun, but it had no shot against a healthy Miami. If the Heat big 3 were healthy from the start that was probably a 5 game series at best, just like the Finals were with the Thunder. Lebron was just on another level that year. Wade and Bosh were still very much in their prime. There are real arguments that if healthy Miami would have had the 3 best players in that series. Bosh being injured and out is the only reason that series was close.