I fear in that case Iraq would join forces with Syrian and Jordan. They have no love for Israel, and our guys would be in deep. Of course it wouldn't be the first "March of the 10,000" in that part of the world. :)
An amazing story.
Iraq itself was at war with half the middle east, including Iran. I doubt they would join sides with them right now.
I don't think that Iraq would do that, not if Iran were attacking them, and us. Our guys would be between a rock and a hard place though. Do we go into Syria to defend Israel, or stay in Iraq to fight Iran? We couldn't let Iran take Iraq, so we couldn't defend Israel if Iran attacked Iraq.
And I completely forgot about Turkey. That whole area is going to explode. If the Syrians and Iranians are going to attack, they have to do it before Iraq is stable. If they wait too long, they will lose their initiative. I actually think that this is good planning on their part. It's either now, or never.