Do you mean the rotor shields? Not the brake ducts that clip on to the rear suspension?
I've had the big shields off on the front since new, with the little tomahawk shaped track shield installed instead, and both shields off on the back for the last year. I did not put the plastic ducts onto the rear suspension. No negative effects in my experience from getting rid of the shields, obviously just one data point. Camaro ss 1le and ZL1 1LE ship from the factory with a front rotor shield very similar to our tomahawk track shield. I think the ZL1 shield might be exactly the same.
While it's not like the brakes are going to fail your first time out with the shields on, the front brakes take quite a beating and could certainly use the cooling help if you were starting to push on track especially on a heavy brake wear track. I don't know how needed it is in back, the pads in back last way longer on track then the fronts.
It's apparently possible to remove the rear shields without pulling the rotors. Mirza the CT4 engineer had a post about that and the whole issue of brake cooling on a different forum, I think it was the forum for V Club. Apparently if you pull the pads and remove the rotor screw, you could wiggle the rotor to get enough clearance to remove the bolts holding on the rotor shields. Which is good because the rear rotors are a bit of a pain to remove. Fronts are straightforward.