Tough but good question. Its hard to assume that if it had released later the RROD would have been fixed. Based on taking the safe road and assuming the worst (that the RROD would have happened anyway just at a later time) I think getting the console out sooner brought the 360 into the public eye.
Now even if the 360 did not have the RROD and released closer to to the PS3 and Wii then I don't think it would have done as well. Let's face it, where would the marketing tactics be? The face of the 360 was the shooterbox and it still wouldn't have gotten rid of that image and therfore people would be willing to buy the PS3 even more especially touting is superiority even though it was blown way out of proportion.
Releasing it one year earlier allowed people to see what MS had to offer the market and it got a lot of exposure. MS took an image hit with the RROD but it didn't stop the entire advantage that MS had with the headstart. Fast forward to now and MS has the largest and most diverse game library. (opinion, not a fact necessarily)
The headstart gave MS more of an advantage than a disadvantage and lets face it. If it was for the RROD the console race would be a fair amount different as far as hardware sales. The places (1st, 2nd, 3rd,) would be the same but the 360 would have sold a fair amount more of hardware. And for the Nintendo fans: Am I saying without the RROD the 360 would have outsold the Wii? That would be a hell no :P The Wii is the sales god this gen.
Consoles Owned: Sega Genesis, NES, PS2 (RIP) N64, Xbox, Xbox 360, PS3, Wii
"In individuals, insanity is rare; but in groups, parties, nations, and epochs it is rule."
~ Friedrich Nietzsche