Here's why Gore would not have invaded Iraq:
1. Assuming this alternate timeline, I still say that Republicans keep/expand their hold on Congress in 2002, and while its pretty inconceivable that they'd roadblock the hawkishness of this magical Gore administration you've conjured, they obviously don't grant Gore the lattitude that was afforded Bush.
2. Gore stays within the framework of the UN. He ratchets up 'inspections', and this is where the hawkish pressure is channeled. It may lead to posturing, which Gore hopes looks JFK-like, wherein Americans rattle sabers in Saudi Arabian bases, but no one crosses the borders.
3. Except maybe some missiles. They don't do anything worthwhile.
4. As a result, the focus shifts to Afghanistan/Pakistan. If American troops are deployed in Iraq-numbers, it is to this region. Saddam Hussein remains in power, etc., etc.
5. This is all moot, because President Dole would've prevented 9/11.