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You have to cut the shroud. That is how you will get cooler ambient air, which is the benefit of a true CAI and the VR. Other air intakes with larger filters are just pulling the heated air from inside the engine bay and many are skeptical as to whether they offer any performance improvement. I believe VR also offers a pre-cut replacement shroud so you don't have to cut yours. But I have heard it is a giant PITA to remove/install. Many opt to cut their stock shroud, but be cautious not to cut the AC line behind it. If you're nervous, have a shop install it for you.
You could also search for the "toggle bolt mod" for the LS2. Basically you drill a couple of holes in the lower section of the shroud and prop it open with toggle bolts. Some have reported decent results from this and it'll only cost you a few dollar$.
You will have to butcher the radiator shroud, and there wont be much left of it. However, its a $50 part if you decide to undo the damage later on. If you don't want to go that route, I'm pretty sure you could get similar gains, for not a whole lot more money, and a lot better throttle response, from a tune by a reputable tuner and not have to cut anything up.