According to this article, proposed changes to the current E-Verify system would allow DHS to have access and if that happens, it seems reasonable to believe that TSA would start using it.

Considering TSA's history, and if the error percentage is correct as stated in the article, I'm concerned that it's just another way for people to be improperly targeted when they fly.

Fortunately, it appears that there's enough opposition across the political spectrum that it won't happen.