if the shockwave change of the dynamic pressure reduces that effect the horizontal stabilizer sees less downwash, produces less down force, and the nose tucks under, increasing descent rate, increasing speed, increasing the strength of the shockwave
According to "Aero for Naval Aviators" and NASA the normal CoP is generally at about 25% chord, supersonic it moves to generally about 50%, that being the case I think CoP movement would have far greater effect than the change in downwash on the tail, hence effects at the tail generally don't get mentiponed.