If it clears the X-ray, I wouldn't be surprised.

If it can't clear the X-ray then it's too big to be screened and obviously doesn't meet sizer dimensions from the airlines.

If it does then passengers could make the TSA out to be the bad guy, which they get enough of already. If it's an issue of boarding time/fit then it's an issue for the airline GA or FA, if they're willing to put staff before the security lines (either airline hired or airport hired) then the TSA still doesn't have to take the heat for it.

I've seen some huge bags come onto planes, not just outside of sizer but plainly obvious that it would not fit into overhead...