A sax is really easy to control (or lose control) of the pitch. And in fact, many saxophonists will just shift various ranges around sharp or flat to suit their style (cough Phil Woods cough).

So basically, a woodwind like a sax will tune a few notes with a piano or whatever, but it's really up to the player to keep playing in tune. I would not even bother trying to autotune or use post-processing; it'll just sound weird.

This is also how you can get a room full of student musicians "tuned" but it still sounds like a disaster.