You may be able to use your benefits if you are paying your way through their Academy. I'm not sure if it would be considered full time or not, because I didn't use mine during the academy. I paid my way through Los Medanos Academy right after leaving the military, and collected unemployment retraining benefits because I was changing my career from Diesel Mechanic to Law Enforcement. If you are just getting out of the Military, speak to the Veterans Benefits advisor at the unemployment office (Employment Development Dept.) and the GI Bill Coordinator at which ever college accredidates LAPD Academy.
It has been over ten years since I went through this, but I remember being told that I could collect one or the other but not both. My checks were about fifty percent of my base military salary, not a lot, but it sure helped keep things together while I was in the academy. You can also try the Department of Veterans Affairs for information. Good Luck to you.
"It's snowing still," said Eeyore gloomily. "So it is." "And freezing." "Is it?" "Yes," said Eeyore. "However," he said, brightening up a little, "we haven't had an earthquake lately."
-- A. A. Milne