Re: bringing an outside cat in
Yes, I think he'll eventually learn to use the litterbox. Your best bet would be to clean the pee-spot on the carpet with an enzymatic cleaner designed for cleaning up pet accidents. The enzymes break down the odor causing bacteria and remove all traces of scent so the cat doesn't come back and associate that area as a 'bathroom' area because of any lingering scent.
When I bring in outside cats, I like to put a pee-clump and a doodie from my other cats, on top of the litter so the new cat can sniff and learn *that* is where they should do their business. With a new cat...maybe you could sop up some of the pee-spot with some toilet paper and leave some of the pee'd TP in the litterbox as a scent-marker for him?
Cats really are fastidious and like to be neat. I think he just has to learn to recognize that "the box" is now where he needs to go.
Best of luck,