Are you going to do it like HIIT? As in sprint 2 sets, walk 1 or some variation of that? I don't really see you doing steady cardio on stairs for too long. I remember we had to do these for wrestling; they were brutal.
I don't know about doing these on a leg day. One flight of stairs is usually a moderate challenge to me after leg day. If you're doing sprints on the same day, then you're training legs incorrectly.
Also, be careful with these if you're packing on weight. If you're starting to feel pain in your shins or legs, stop doing them.