He certainly jumped on fiberglass backing for his bows as soon as it was available, which indicates that he wasn't stuck in the past. He makes it clear in his books that he shot the straight longbow because he thought it was the most dependable bow available. He tried recurves, but the ones he tried shot erratically for him, so he stuck with longbows. But I believe if he could have shot recurves better than he shot longbows, he would have been a recurve shooter.
Based on his history of trying new things and using those that he believed were an improvement, I have no doubt that he would have tried carbon arrows and would have used them if he believed they shot better than wood arrows.