Reagan would have recognized that Iraq was a strategic threat, and that it was the heart of the Islamic world, and Reagan would have followed GWs actions, Reagan would not have merely gone into Afghanistan and played cat and mouse with guerrillas, in the mountains to no real end or result.
Reagan had waited out the Soviets. Why wouldn't he have waited out the Iraqis? The Iraqis were a perfect counterforce to the Iranians. Why get rid of that? The cost of maintaining the no-fly zone for decades would have been chump change compared to what we spent to make Iraq safe for ultimate Iranian takeover.
What kind of a strategic outcome is that?
It's interesting that, in her book "A Problem from Hell: America in the Age of Genocide," Samantha Powers—who famously pushed Obama into this Libyan misadventure over "responsibility to protect"—criticized Reagan for not doing more when Saddam gassed the Kurds in early '88 during the Iraq-Iran war.
While his administration condemned the use of chemical weapons—Reagan had called for and negotiated towards an int'l ban—we continued an active trade policy because Iraq was a large importer of agricultural goods and seen as a counter to Iran.
In light of the Cold War overshadowing the choices he options he had, it's difficult to say how he'd have reacted post 9/11.
I do believe, however, he wouldn't have wasted precious time on war college fantasies about reduced troop levels and would've opted for a larger force, avoiding the need for any surges later. I think he'd have stayed focused on Afghanistan and kept a close eye on Iraq.
We may have been pulled into engaging Iraq but I don't believe the time table would've been the same.