Even of it is B to B, which I'm pretty sure it is not, it is a different pier and different security to clear. All the little planes except a few of the EMB-170s (or whatever US's larger RJs are) go from the same lower level C gate.
It would probably be a little too close for me. I do believe that they have the flat tire rule. Just tell them you got stuck in traffic... just don't mention it was on the taxiway in ATL.