If we each knew that the other had 'SA' and both knew that the other knew, then it would be pretty disastrous.
As soon as someone places that label on me, they have certain expectations of how I will be. Once I've been defined as socially underwhelming, I have no reason to exceed those expectations or step outside the comfort zone of being just what they expected.
"woops, I don't want to be too talkative.. I'm SA after all!"
If we both knew, but didn't know that the other knew, then it would probably work out quite well, as we could be empathetic to the other's feelings, without making an obvious spectacle of it: "oh, I know that you have SA, so I'm going to talk real, real soft to you and be super sensitive"