Jane, applicants can put whatever they want on their résumés, but if a company actually decides to use that information in their hiring process, and a disparate impact results, then litigation would likely ensue.
By the way, disparate-impact litigation is a prime example of how obscure legal doctrines (not obscure to employment lawyers, but to virtually everyone else) can have seismic cultural consequences. Outside of the military, it’s tough to think of a single significant employer that screens employees through testing rather than credentialing. And there’s certainly no single test or group of tests that prospective employees can use to enhance their applications with multiple employers. The consequences are obvious: a stampede for credentials, watered-down credentialing processes, and soaring credentialing costs.