Brian,
I would imagine the best bet for you to get a chair spot on 18 on Sunday is to make sure you have an official Masters folding chair before you start to wait in the queue on Sunday morning. Try to get it on Saturday or whenever you would have a chance. There is a merchandise area outside the gates so go there the day before and get one if you can. My point is, if you try to bring your own chair in, than they might not allow it or they might search though it for too long of time. But, if you try to buy one that morning, there's no way you'll be able to do that and get it to a good spot behind 18. Also, as was said earlier, a good amount of the space by 18 green is reserved for members and special guests anyway.
I would also recommend getting there around 7:00am or 7:30 at the latest at the entrance. Account for some traffic and parking time. There will no doubt be boatloads of people there early so if this is your only chance, then make sure you're there early enough. And plus, since there's no running at Augusta, get there early and swiftly walk over to 18, put your chair down with identification on it and go enjoy the day.