AFAIK, the only state that ties inspection to registration is NC. In NC, there no longer is a physical "sticker" on the windshield, but rather you must have the car inspected which, if it passes, means the garage enters that in the DMV computer, during the 60 days leading up to the renewal. No inspection - no renewal. NC did away with actual stickers 10 or so years ago.
Here, in WV, inspections have nothing to do with registration. You are supposed to have a valid "sticker" but probably 1/4th of cars don't. This has nothing to do with the registration. The car comes new with a sticker, so that is the month the car was delivered to the dealer (and thus a way to tell if a particular one has been on the lot a while and they might want to give you a deal) and, if you obey the law, will keep that month forever. It has nothing to do with the month your plate will expire. Oddly a June plate expires June 1, with a June sticker expires June 30.
I think PA is the same. I have seen cars with expired PA stickers, IIRC.