The check engine light will go on when you leave the gas cap off, dirty air cleaner, change the oil at 3,001 miles, remove the cat, sneeze with the top down, run over the neighbors dog, or play country music on the radio.
But seriously, I think it will come on, there are so many sensors on them they can detect everything, and I'm sure it includes the cat. I'd throw on a Borla or Gibson rather than remove the cat. But then again, when our cat blew apart and plugged the exhaust, nothing happened, so you might give it a whirl. We're looking into an aftermarket cat that can withstand the off-roading and reduce the backpressure. We'll install the cat-back at the same time.
JEEPN
'81 CJ-8 Scrambled!
GM151/SM465/NP205 twinstick/7"Lift/33"TSL's/IHC D44's 4.10's Lock'd