Well, Ab7/C is something like Ab, C, Eb, Gb with C on bass.
Cdim(b13) is C, Eb Gb, Ab Bbb(A). It is not the same.
Maybe you could put Ab7/A (A, Ab, C, Eb, Gb) but it is not the same as the bass is different and the pitches will sound against a A and not a C.