I'm a belt and suspenders guy (though cmoulder has inspired me to occasionally leave the suspenders behind). As such, I try to use things as designed. If you sit on that pump bag, my guess is, you are putting many more lbs/square inch on it than it was originally designed for. In addition to puncture, you are also putting stress on seams and seals. That doesn't mean it won't work - for a while. But a simple square of CCF foam is so light and compact; why not use it and eliminate any risk of damage to the pump bag.

Now if the pump bag was advertised as being "chair-able", that would be different.