Your stopover, if there were one, would likely be a fairly grimy MIA airport dump. An unpleasant experience at best, unless you want to shell out for something nice downtown and spend the evening.

But, as others point out, it's highly unlikely that AA would overnight you above putting you on BA. The problem is that not only will you be in steerage, but you'll be seated in whatever seat might be available in steerage because you are a last minute add. While you never know and might get lucky, the likelihood is that you are in Steerage -.