If your test will be run on a Windows machine, you can install NVDA to listen to the site yourself, before the test. It's available for anyone to use, no charge. If you are running the test on a Mac, use Window Eyes.
Is your representative user who is logging in from home a visually impaired user who regularly uses screen readers? Will he be working with his own screen reader remotely?
Any adaptations to your normal testing routine will be dependent on your measurable objectives of the accessibility test.
Just present the participant with the URL of the site, with no instructions other than your task list. You'll want an unbiased case study.
So the compliance you'll need to work with is WCAG. The ADA is mostly about building compliance, such as "ADA seating" or proper wheelchair ramps. When the ADA refers to web site accessibility, they refer developers over to WCAG.