Well...for most of the time, yes. I think when Fulmer was OC under Majors he had it going on. Some of that likely was still Cut, but I don't think Cut and Fulmer completely overlapped either and I'm too lazy to look it up.
But even with Cut back in 06-07 our offensive scheme was often described as boring and predictable. Just saying. IMO it was, but we still had a decent offense because (a) Cut is an excellent developer of QBs and got Ainge to live up to his potential, (b) Cut was known as a strict disciplinarian that the players respected (this is probably the biggest reason), and (c) Cut was calling all the plays.
It's often repeated, but if Cut stays for 2008 Fulmer likely would have lasted longer, maybe a lot longer. Having said that, it's rumored that Cut gave up on Crompton and just didn't want to be around when the **** hit the fan. That may very well be true.