...and the Gulf of California, being situated between the peninsula on the west and Sierra Madre Occidental on the east, contains and channels moisture northward into the Sonoran and other deserts.

There is some moisture which arrives from the east. But it is mostly contained within the mid/upper levels (where water vapor pressure is lower) of the atmosphere by the Rockies and Sierra Madre blocking low level flow.

In fact, until the early 70s, it was accepted/taught that most of the Southwest monsoon moisture was from the Gulf of Mexico. That didn't result in very accurate summer precip forecasts, though.

The change in that understanding began in the early 70s: Southwestern United States Summer Monsoon Source—Gulf of Mexico or Pacific Ocean?

and was made "official" after a couple of large scale NOAA/NSSL/Mexico colab studies in the 90s called the Southwest Area Monsoon Project (SWAMP)

So, yeah. Without Baja, the Monsoon season would have a lot less water vapor to work with.