Does the action ever wear out?

90% of rifles in the hands of a civilian... No

Military M40's and M24's... Yes. Trigger pin holes can become worn & loose, I'd imagine after truing a few times the integral lugs would be worn back to being out of spec, the face of the receiver would become too short also.
 
Theoretically that is true. But most gunsmiths who are doing a build will retrue it to their specs if the rifle is new to them. If you keep sending back to the same shop it shouldn't be a problem.