Sure, I've done it several times.
Of course Sea of Cortez scuba is like eastern Pacific rather than Caribbean diving, so don't expect reefs lush with colorful coral & sponges, or big vis. Tends to be rocky with sand & rubble bottom, with 40'-80' vis.
Bless the Don Jose--it's been around a long time. A big, lumbering wooden craft with 7 A/C cabins, it's quite stable & seaworthy if not snappy. More room than many live aboards.
Earlier in the season, like Mar-Jun is whaleshark time, and later in year the water warms up quite a bit. But, it's fun diving all the time. Los Islotes consistently delivers the sea lions, and El Bajo often has hammerheads & mantas.
Old Don Jose is still the captain, Luis & Felix run the pangas, Hernan does the mechanicals & Enrique, assisted by Dios, turns out tasty & visually appealing food. They are very, very nice folks.
La Paz is still a relatively unspoiled Mexican fishing village on it's way to tourist development. Couple of good seafood restaurants.
Best regards.
DocVikingo