I've had it happen both ways, as a lot of time I'll do a one-day rental with a free day and then drop off and pick up again. BHM was an absolute NO with a base Impala (but I was only EA at the time and not ES), but at Washington Union Station the station manager happened to be there and was more than happy to upgrade me back into the Jeep Grand Cherokee that I had picked up at BWI a couple of days earlier.
The last one was fortuitous as later that week was one of the big DC snowstorms, and I spent 5 hours in that Grand Cherokee on the Dulles Access Road local lanes behind a bus jackknife.