Probably having NO Cats, but that's also a Federal Offense. Everything else is at the whim of the service manager, but legally the modification has to be proved by the service manager (or dealer or DC Regional Rep) to have caused the claim for warranty work before they can deny your claim. Some will work with you and some...well, should be flushed down a commode...
If you have a regular cheap Viper and put K&N filters & smooth tubes on and your tranny breaks, they could deny your warranty claim because you didn't keep your Viper stock. You then appeal and state the ACR Viper has the same mods as your Viper and it is covered under warranty, then the appeal process will rule in your favor and have your tranny fixed under warranty.
If you have a lot of "neccessary" mods and something goes wrong it probably will be tougher to win your appeal, but the company side that's denying your claim still has to prove that the supercharger (for example) you put on caused the problem with your a.) tranny or b.) radio. In the case of a.) tranny, it might be tough to prove having 800 rear wheel horsepower didn't cause the tranny to fail. In the case of b.) radio, it would be pretty easy to prove the supercharger had nothing to do with the radio being stuck on the all polka station and you'd win easily.