Not a chance.
A psychological condition / impairment would be covered by the ADA.
But the airlines are not testing for that, and even if they found such a condition it would almost certainly invalidate your medical anyway. They are allowed to verify that you meet 1C standards, they just cannot apply their own, higher, medical standards any longer.
What they are testing for is personality factors, to determine your suitability for their job, culture, organization and that is perfectly legal. I happen to think it's BS that they're allowed to do that, because it imprecisely excludes too many folks who would be just fine. They could make a much better determination at a face-to-face interview, but of course that's expensive.
But not being a good "fit" for their culture is not a disability.