If there was a civil war in Iraq as the result of Arab Spring, would US and allies intervene?

So, let's say for some reason, 9/11 never happens and there is no war in Iraq. As Iraq continues to fail economically, the US and it's allies maintain the no-fly zones established after the Gulf War.

Flash forward to the Arab Spring. A protest movement among the country's Shia majority, located in the south of the country, spreads like wildfire in the country. Desperate to hold onto power and seeing his rival Syria descend into chaos, Saddam sends the military in. Somehow, the Shi'ites acquire weapons (maybe they get them from Iran or sympathetic elements within the Iraqi Army) and begins fighting the Iraqi Army in cities like Basra, giving Saddam the excuse to send the Air Force in.

Now, here's my question. Would the US and it's allies use Saddam's crackdown on the Shi'ite rebellion as an excuse to bring down the Ba'athist regime? According to the US, they had the legal right to establish no-fly zones under UN Security Council Resolution 688, (though the resolution made no references to no-fly zones), so would they act on this supposed legal authority to help bring down the regime? Or would they leave the Shi'ites to their fate since there's a chance they could be backed by Iran?

And what about the Kurds? Would the US and it's allies intervene to protect them since the Kurdish region was also covered by a no-fly zone?
 
Probably go and intervene for the Kurds. Not sure for the rest though it depends on who makes the West a good deal
 
In all likelihood the no-fly zones and the sanctions aren't there anymore or ineffective as both Russia and China had been arguing in favour of lifting the sanctions in the early 2000s. If Russia and/or China help Saddam get his army up to speed again, he's going to make Assad look like an innocent choir boy if something like the Arab Spring still happens despite the butterflies. I imagine the US and its allies would support the anti-Ba'ath opposition, which in both Iraq and Syria will have the benefit of not having to worry about ISIL. Lack of ISIL is offset by Saddam's cruelty in what will be an ugly civil war with an uncertain outcome.
 
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