To add to the other comments here about how Iraq probably wasn't inevitable, a full-scale invasion and occupation of Afghanistan may also have been avoidable. It would have more likely happened than not, but there's maybe a 30-40% chance that a Gore administration would have opted for (1) the pre-invasion Taliban offer to turn bin Laden over, (2) the post-invasion Taliban offer to end the war quickly, or (3) a global manhunt for bin Laden instead of an invasion/occupation.

The difference goes back to the response to Vietnam. Democrats tend to admit we lost that war, and want to avoid getting in (and losing) another Vietnam-type war. They're still fine with imperialism (even if they would argue with calling it that), they just want to do it less directly. This is still awful, but at least it's less destructive. Republicans, on the other hand, will give you nonsense like "we didn't lose Vietnam, we quit/we set too many restraints on our military/the hippies undermined the war effort." Between the exit from Vietnam and 9/11, they'd talk about how we needed to kick "Vietnam syndrome" so we could more actively (which means more destructively) do imperialism. Republicans want an honest-to-goodness American Empire; Democrats want to do neocolonialism and smaller "interventions."

The distinction has been blurred a bit in the 20 years of post-9/11 war, but it was pretty clear in the late-90s/early-00s. Gore would have at least strongly considered smaller-scale responses to 9/11, even if it's ultimately more likely than not he would have invaded Afghanistan (due to the shock of the attack, pressure from the military-industrial complex, how easily libs turn into hawks, etc.).