Yes, one may keep that in mind when working something on scratch paper. But when it’s possible for things to be complex, the standard notation is something like

Yes, one may keep that in mind when working something on scratch paper. But when it’s possible for things to be complex, the standard notation is something like A^. In my opinion, it is rather sloppy to write A^T and expect the reader to substitute for the complex case. I can’t remeber where at the moment, but I have definitely seen derivations when the authors explicitly wanted A^T on a complex matrix.