I experienced the same issue as BDP Mike when I drove my car at triple digits speeds with my 2010 when the under cover was removed... The hood was shaking and not felt safe at all. Maybe it is different with the 2013 with the hood being different? That said, I prefer to keep it for protection from rocks or other things that could damage internal parts. Also, I believe that the airflow and aerodynamic is probably better with it. With Tstat170F and tune, my water temps are always under 180F regardless of the outside temperature. Even now, with temperatures in the 20's, it is always between 170-180F.
So, I really don't think the under cover has anything to do with engine performance. The faster you go, the more air you get and it evacuates anyways. When you drive at 140 mph, even with the undercover, the air is evacuating very fast believe me.
I ran at the track many many many many times (500+) with the 2010 and 2013 SHOs with and without the under cover and it makes no difference at all, beside the risk of damages and perhaps hood shaking and aerodynamic not as efficient.
Engine cover however is a different thing I think. It doesn't hurt the aerodynamics when removed, heat can evacuate better especially when not driving fast (between runs or at idle) and you save 1lb! lol