I'm all for interesting scenarios which might have expanded the reach of the United States, but this is too far and patently absurd. Were the U.S. to capture the region, one suspects it would be given to Morocco anyway. This would be more pointless than the U.S. taking Spanish Guinea, and even that is absurd.
See below:
Even though the OP asked to avoid discussing the why and how I'd like to point out the above as a good reason for annexing the Spanish Sahara.
Given the USA's history and good relations with Morroco a POD could be set up to have the USA take the Spanish Sahara away from Spain as a means to maintain Moroccon independence and American interests in Northwest Africa and the Strait of Gibraltar.
After taking the Spanish Sahara I'd imaging that it would be put into a similar position as Cuba, or the Phillipines. But eventually the USA may cede the territory to Morroco.
Wikipedia: Morocco-US Relations; Later 19th said: