You'll be allowed to park in Curry Village or at trailhead parking. I don't believe they bother to check cars for anything other than coolers, cups or other things that might entice bears to break into your car (you will get a stiff fine for a bear break-in if it happens so it's worth cleaning your car). There are cars sitting in the lot covered with grime, obviously been there a good long time.
However, YARTS will be running only for weekends in September and not at all after that. Not sure when you intend to go, but I'd check on all shuttle schedules if you haven't already - YARTs, the shuttle to Reds/Agnew, all of 'em. I'm sure the one to Mammoth Ski Resort will run.