Body roll is minimum. My Abarth has quite a bit of body roll going into corners...enough that you wish the seats had more bolstering. The Alfa has absolutely zero body roll. The Elantra Sport definitely leans towards the Alfa end of the spectrum.
The dealer's test track is probably about the size of a football field, with one side being coned like an autocross track and the other side left as a fairly decent straightaway. While in the autocross section of the track (with lower speed, of course) I could detect almost no body roll at all. When entering the turn at the end of the straightaway, there was some very, very minor body roll, but I was going fast enough to wag the rear end with traction control on, so I think you'd have to be really flogging the throttle thru the turns for the body roll to be noticeable. Now since the GT Sport will be a little taller, there might be some additional body roll, but I'm inclined to think it will be negligible, especially since the cars share the same rear suspension.
I bought my Fiesta ST from the same dealer, and they let me take that car on the track too. Probably sealed the deal. Hopefully, when they get some GT Sports in stock, they'll let me repeat the drive in one of those, then I can report back with my impressions. The waiting is annoying, especially with the sedan already available and being so good. My wife might have bought the one we test drove if it wasn't red (not her favorite color). This has the potential to be a pretty outstanding ride if they did it right.