I'm pretty sure that you cannot. I have seen some of the specifications on those bags and they have a very stern stipulation that they only protect things INSIDE the bag.

Honestly I don't know why you'd need an anti-static mat. Just keep hardware inside bags or on some other low static surface. The hardware shouldn't be out on the desk anyway. The only reason I could see needing the anti-static mat is if you were doing electronics work with loose parts (i.e. individual chips) which you needed to keep from being exposed to static.

View the original article here