I would like to use localStorage/sessionStorage to store essential information during a commerce process, which includes site reloads/redirects. Forms are not an option.
That implies, that the user has to have JavaScript enabled. That fact and the usage of these techniques, could it affect accessibility tools, for instance screen readers?
I could not found any information in the WAI-ARIA specification.
This is no longer considered as being a problem.
This is documented in the WCAG FAQ : Can I meet WCAG 2.0 with Javascript/Ajax, Flash, PDF, Silverlight, and other technologies?
More information can be read in the conformance claim chapter
Javascript is considered nowadays as being "Accessibility Supported" but you would have to explicity state that this technology is "relied upon" in any conformance claim you may establish.