It would be unnecessary and could potentially actually reduce its shelf life while altering the flavor and texture in possibly undesirable ways.

You could, but there's really no need. The salt used in the brine brings the PH to a spot which is really inhospitable to bad bugs.

Salt doesn't change the PH.

The fermentation produces acid though.

True, salinity !== alkalinity

Not only that, but salt and capsaicin -- the thing that makes hot peppers hot -- both tend to kill stuff.