Depends on what kind of pad. If it's the kind of pad that where you reduce the polarization voltage of the capsule it shouldn't change the sound in any way. I'd say claims about this type changing the sound are urban legend.
Adding a cap somewhere in the hiZ area (there are different arrangements) will change the sound, but how much could be debated. Recent thread started by MicUlli points to possibility of even rising the THD by doing so. It will prevent the first stage from clipping tho.
There are some mics that have a pad in the end of the circuit, which just prevents preamp to clip. It doesn't really pad the first stage of the mic, so it might still clip, but might change the sound by altering the mic/pre interaction. Depending again on what kind of pad it is, where in the circuit, transformer or not.