Am I able to continue receiving unemployment while waiting on my disability claim?

Yes you can. In fact, You can collect both unemployment and SS disability at the same time. Unemployment benefits are not counted as wages under the SS annual earnings test, so it won’t affect your SS benefits. However, the amount of your unemployment benefit could be reduced if you receive SS benefits (or other pension or retirement income). I have provided links to 2 sites that will explain further:
 
www.socialsecurity.gov/pubs/10069.html.

http://www.ssa.gov/policy/docs/progdesc/sspus/unemploy.pdf