It most likely will be affected by Mach Tuck. Although I am no "Boeing expert", I just took a look at a "comparable aircraft". The tendency to have adverse pitch stability above a certain Mach number is more or less inevitable for subsonic profiles. Additional effect is that the elevator will lose efficiency quite quick when going over MMO and ultimately MD.
And it actually goes quite quick: the pitch stability switches sign within 0.03 Mach counts.