There are strong arguments made that Gore would've invaded. I found some in Iraq War - Gore Would Have Done The Same As Bush, Says Study:
...Dalhousie political scientist Frank Harvey in a paper for the Canadian Defence and Foreign Affairs Institute (CDFAI) ... argues Gore would have invaded Iraq just as President Bush did, and in doing so, pieces together what he considers to be a stronger explanation of the decision to invade in the first place."A pdf of his paper is here: President Al Gore and the 2003 Iraq War: A Counterfactual Critique of
Conventional “W”isdom by Frank Harvey, PhD.
Harvey also wrote a book published by Cambridge University Press, Explaining the Iraq War: Counterfactual Theory, Logic and Evidence. Here's a video of him talking about it:
A shorter, more informal argument is made in Why President Gore might have gone into Iraq after 9/11, too - Salon.com:
...President Gore would have been hearing the same pleas. His own vice president would have been Joe Lieberman, perhaps the most hawkish Democrat in Washington on Middle East issues. Marty Peretz, his old friend and confidante, would have had Gore’s ear and filled it with arguments for going into Iraq. Loud, influential, non-conservative media voices — like Tom Friedman and Peter Beinart — would have amplified these calls on the outside. Republicans would have been screaming for an invasion, and the public would have been on their side. Clinton could barely hold them all back in the ‘90s; after 9/11, would Gore have stood a chance?
Here it’s worth remembering Gore’s own history. In the 1980s, he made his name as a senator and presidential candidate by positioning himself as one of his party’s foremost hawks. One of the reasons, in fact, that Clinton put him on the Democratic ticket in 1992 was Gore’s vote for the Gulf War, which most Democrats had opposed. You could argue that Gore was a changed man by 2001 and 2002, and that he saw the world in a fundamentally different way, and maybe that’s true.
But it should be noted that when he announced his opposition to Bush’s war push in the fall of ’02, Gore endorsed the basic goal of removing Hussein and securing his (supposed) WMD stockpiles. What he objected to was more the go-it-alone nature of Bush’s approach. In other words, you could also argue that Gore, still stung by the 2000 election outcome, may have been motivated in some way by his desire to stage a big, principled fight with Bush — and that a different result in ’00 might have produced a different, more hawkish response from Gore, one that would have led to … an invasion of Iraq.