Distinguished SOTW Member/Mouthpiece Maker
I'm pretty sure it doesn't. Fortunately, we don't need to argue about it, this is easy to test. Make yourself a Helmholtz resonator for which you can alter the shape of the chamber leaving everything else the same. For instance, take a mouthpiece sealed at the reed end, some putty, and a tube in the other end. Move the putty to various places and examine the pitch as you blow across the top like a bottle.The basic Helmholtz model remains valid.
With a large chamber tenor piece, 4cc or so of putty, and a neck about 13mm X 70mm inserted up to the throat, I can vary the pitch by as much as a half step depending on where the putty is (long baffle, very large throat is ~340Hz, short baffle, medium throat (still larger than neck bore) is ~320Hz). This is in a Helmholtz resonator with constant chamber volume and length, and constant port diameter and length.