First off, welcome back to the BBS... Good to see you around again.
I don't think UN would have complained too loudly, if at all. Methods Coalition forces employed were rather far from impeccable (remember Basra road with its 'collareral damage', fabricated news of Iraqi soldiers plundering matenity ward of Kuwait hospital leaving babies on the floor etc), but there was virtually no outcry and that was basically considered (perhaps correctly) as grim but acceptable price to be paid for liberation of Kuwait (whatever that might mean, given the regime there).
I'm not sure how all the fabrications and collateral damage during Desert Storm relate to the question of whether the U.S. and its allies would have been allowed to keep going once Kuwait was liberated. Once the job was done, there was no chance of being given International support to keep going. There was already spotty participation from some of the coalition countries, and they were only there because of the U.N. resolutions, resolutions which were passed solely to get Iraq out of Kuwait. I can't imagine any scenario in which further U.N. resolutions would have been passed to keep the coalition together for an assault on Saddam Hussein's regime.

Incidentally, though Kuwait is not exactly a shining example of democracy, there are competitive elections, a Parliament, etc. It's really the only Arab state in the Gulf with anything resembling a legitimate political system.
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- Tony C
my empeg stuff