The launch would be to an orbit that would decay in a short-ish time (perhaps fairly elliptical?), since SpaceX wouldn't want to leave the second stage up there

The launch would be to an orbit that would decay in a short-ish time (perhaps fairly elliptical?), since SpaceX wouldn't want to leave the second stage up there long term as yet another large piece of space debris. Talking from the knowledge of a hobbyist here though, rather than an expert on such matters, so probably wrong on some counts.