It has happened, but is not typical. Possible LAX NH categories are 7ER (757/767 ‘classic’ - no current vacancies), 737, and 320. Someone posted the possible vacancies from which they may pull in the
DL Hiring:New Process thread
Your best bet is to AE to LAX in the 73 or 320. Otherwise, you will have to wait a year to get to LAX if you get the 717 or 220, as they are not in LAX.