I do. I live in california and I collect 1800 a month from unemployment and my Gi Bill gives me 1700 for BAH..So legally you can because that BAH is non taxable income, also the fact that your not "working" to earn that money, it is a benefit for your service. I asked the unemployment office about this and they said as long as your actively looking for a job you can collect. As long as you don't go to school during normal work hours. Typically 8-5pm is a normal work day. But I got to school 6pm-10pm. So my school doesnt interfere with normal work hours. See how I worked that? So its all good!
I collected unemployment upon returning from my first tour in 2007 as well as the Montgomery GI Bill. I had to prove that I was still able to work as a full time student (I took classes in the mornings and evenings so that I could work during the day). I'm trying to find out if anything has changed with the Post 911 GI Bill myself, but as of 2007 I was able to. Just make sure you can prove that you can still work as a full time student. Hope that helps!