I don't believe they were ever in the military, but if your story can have some way to make it fit, okay. But make it a reasonable explanation, because Sangheili are trained FROM BIRTH in their future career.
As for everyone else, Jackal females fight, Yan'me fight and become queens, Grunts are suicide bombers and baby makers, and Hunters are worms. Brutes I don't know about.
Also, I think Sangheili females might be kinda like Spartan women, so while all the dudes were fighting, they were selling stuff in markets, farming, doing other jobs, etc.
[Edited on 01.26.2011 6:08 PM PST]