I'm afraid I've never used the GAC myself, so can't offer you personal experiences, but it might be able to help. The accommodations provided by the GAC vary, depending on your needs. It's not a way to skip a queue (I know you're not asking for that, I just don't want anyone reading this to get the wrong idea), but for some attraction you may be able, for instance, to wait in an alternative area out of the sun. As I say, I've never done this myself, so don't know first-hand.
OK, now I'm going to veer OT a little bit, to make sure you know about other help you can get at Disney.
Firstly, you said he gets tired easily. You may well already be planning to use one, but a stroller will help to conserve his energy for the fun stuff, and give him somewhere to nap if he needs. If you use one with a canopy, it will also give him some shade. If he would benefit from a lie down in the air-con, the First Aid stations at each park have beds that you can use as you need.
Make sure you pace yourselves. I'm sure you're used to doing this by now, but it can be harder at Disney. A lot of people find it helps to go back to the hotel around lunch time, for a bit of down time. A short swim, watching cartoons in the room, or a brief nap can do wonders. It will also mean you're not in the parks for the hottest part of the day.
There have been a couple of threads in the past about keeping cool in Florida. You could probably find them on a search, but I'll see if I can dig a link out for you. Most of the things are fairly common sense, but their may be some useful little gems in their.
Good luck and have a great time!