Two real reasons why not. One, the CSA didn't have any control over anything in Arizona/New Mexico (which aren't even divided), so it's hard for them to claim the land. Second, Britain was hoping to chop down the US without making it overly hostile. Since D.C. was still American, and Lee's invasion of Maryland didn't get the support of the Marylanders that the CSA had been hoping for, it wouldn't have really been in the cards to isolate the US capital by seizing all the unwilling land around it.
Yes but with such a victory, the Marylanders would be more eager. Yoru right;the C.S didn't get their support-in OTL. Not just because the Southern troops didn't have shoes, or nthe music wasn't nice enough, but also because the CS failed in its objectives and was forced back.