the mouthpiece is pretty much an instrument unto itself. though there may be an "optimal" note for each saxophone, it can't hurt to be able to play the crap out of your mouthpiece.
you can get some AWESOME exercise and control by learning to use your throat, mouth, and embouchure to manipulate the pitch of just the mouthpiece.
after a bit of practice you should be able to get about an octave (maybe more!) out of it.
practice scales, scale exercises, simple melodies. it all helps.
not only are you basically "lifting weights" for you embouchure muscles, but you're also doing some good ear training work!