No, they don’t, @flatKansas, although they (almost?) all have them nearby: http://bamadining.ua.edu/locations/
I believe the Common App asks you to agree that you will not make deposits at multiple schools that use the Common App. Alabama does not use the Common App, so ds felt free to deposit at UA. As it ended up ds loved UA and he did not deposit at any other school, but I think he would have been free to do so if he wanted to. Alabama does not ask you to agree to not deposit at another school, and they know some will change their mind. One of ds’s initial roommates chose another school after room assignments were completed.
That may be the general inference, @BlessedMom3, but the document my son and I both signed did not distinguish between common app schools and any other.
I agree with you, @LucieTheLakie. The good thing is that most schools do not determine housing the way UA does (at least the ones ds was applying to) so students will not have to worry about the double deposit issue.