I will say that a GAC will almost never reduce distance walked or the amount of standing. I have had nearly every stamp on my GAC (and I use a wheelchair and I have been to all American Disney parks and have used a GAC at both), so I can tell you that it can help with invisible issues that are
not stamina or mobility based. For those, the best thing you can do is rent a wheelchair,
ECV, walker, knee walker, use a cane, crutches, etc. Honestly, most people would rent an ECV.
GACs do not help with character lines (almost all of them anyway), distances between attractions, restaurants, stores, parades, fireworks, shows (have to wait for the next show no matter what, and for things like Ellen, that is 45 minutes), bus lines, anything at the resorts, or DTD.
The distance walked around the Showcase Lagoon is 1.25 miles, and that is before you walk into a single pavilion. Walking from the bus, up the hill to the Land Pavilion, down into Soarin, ride Soarin, back out, and then to the bus again, and you have walked almost 2 miles. The queue is 1/4 mile in and 1/4 mile out once you get
into the pavilion, and no GAC can shorten that.
I would suggest looking into
ECVs and wheelchair. What I have known some people to do is to rent a wheelchair, push it empty through the parks and then sit in queues (where the ground tends to be flat and therefore easy to be pushed by others) or while waiting for parades or fireworks
I would still consider speaking to the Guest Relations folks about a GAC (you may find avoiding stairs helpful - it would not shorten your wait or distance walked, but it could help if standing on stairs is too difficult), but you should know that a lot of people with stamina or mobility concerns have not found a GAC entirely helpful for the amount of distance walking required in WDW.