I’d be for it, and make it a bastion of pro-Americanism in a bad neighborhood. Support them to the hilt, starting with an air bridge of supplies, advisers, and FACs. They have earned nationhood, IMHO, and they are 100X more reliable than Iraqis.
My guess is Baghdad will fall before the end of the year. You can’t defend any city with Sunni troops, not when half of them will defect to ISIS at the first chance, and the rest will run away. At “best” Baghdad will be another bloodbath, with a war between the Sunnis and Shias. At worst, the Sunnis will drive out or mass-murder the non-Sunnis, and Abu-Bakr al-BAGHDADI will install himself as Caliph, with Baghdad the capital of the Caliphate.
If this happens, Katie bar the door. We may see a shockingly rapid advance of the Caliphate, including in Jordan, Egypt, Libya, Algeria, etc.
Baghdad will be a bloody fight. The city is fairly evenly split between Shi'ites and Sunnis, and it is HUGE. I can see block-by-block fighting going on for months. Sadr City alone would take forever for ISIS to pacify. Even with air support and heavy armor, we treated Sadr City with respect. The Dora and Jihad regions also come to mind as very tough fights for Sunni invaders. Now that the military is bound to be split along mostly sectarian lines, we're not likely to see another Mosul-style blitzkrieg.
The domino effect is a real concern, you're right. We've already seen it on a fairly large scale after our own government backed the worst horse possible in Egypt. There's no reason to think it won't accelerate if ISIS declares and implements a true caliphate, though I think we're pretty far out from that happening.
For an interesting take on the whole deal, an old friend of mine I served with in the 3d Stryker BDE has written this article with his own thoughts on what to do. He starts with the history of the region, some of the backstory on where AQ and ISIS scumbags come from, and how he thinks we can handle them. I think his solutions are a bit Pollyanna-ish, but the breakdown on why we are where we are is pretty interesting reading.