Patching with a plug and patch inside depends on where the hole is. If the hole is at the tread edge a plug and patch is not recommended because this area works alot with turns, less so in the rear. A reputable shop will not do a plug in this area. The sidewall area for a hole is also a no plug patch area.
That being said I have used plugs in the areas noted in emergency and they have worked for a DD around town but they will eventually leak and the tire needed to be replaced. I usually put the plugged tire in the rear (not doable with a TT ). If the tire is under a road hazard warranty it should be covered for a new tire with some proration depending on the warranty. However if the other same axel tire is worn down to much you should replace in sets for front or rear as the case may be.
