You do not need a GAC with an
ECV in Disneyland. Do not try to leave the ECV outside of attraction lines - the queues are VERY tight are there is absolutely no where to sit once you leave the ECV.
The GAC will not shorten wait times, but the ECV will help a lot. The GAC is intended for invisible disabilities, such as allowing a person with a vision impairment to sit in the front of a theatre or alert a CM to a person with autism.
Even with a GAC you will be required to wait in line with other people with mobility impairments, no matter what GAC you have. This line can be quite long at times, and they will be as long as stand by lines often.
I am a full time wheelchair user, and I keep my wheelchair right up to the ride car, so I have no problems enjoying the park fully.
You will have a great vacation! I suggest renting an ECV off site as they are smaller, easier to drive, and cheaper. Also, you cannot take a park rental into the Downtown Disney area. Park rentals sometimes (often) run out, so you will definitely want your own.