Can you draw unemployment benefits while on appellate leave from the Marines?

Probably varies state by state, but in California, you cannot use your military wages to qualify for unemployment compensation unless you have your DD214. However, if you had another job during the qualifying period, you may be able to use those wages to qualify. The simple answer is - call your local unemployment office and apply. The worst thing they can do is say no, and you just might get lucky and get some money out of it.