Yep. He was indeed a Hawk and wielded US military might. It is not a fair comparison to look at Cold War era deployment of troops and post-Cold War. There is no doubt Reagan would have utilized troops after a 9-11, and in a similar way as Bush did.
I can’t say if he would have gone into Iraq, but I have to imagine that Bush 41’s decisions in 1990 and 1991 were consistent with the Reagan team’s philosophy, and the actions of both Clinton and Bush 41 continued to enforce Hussein’s surrender agreements. I also would assume that Reagan would have been equally as strong against a defiant Hussein when he refused to comply with his surrender agreements after the gulf war. In terms of Reagan, I can only guess that he might have found a way to dispose Iraq of Hussein in a different manner that the ground war that we faced, but I would guess Bush would have too if there was an option out there.