Yep. Static electricity can definitely cause a balloon to pop.
In fact, if you're ever seen balloons (that weren't overinflated) just randomly explode out of nowhere, the culprit was most likely random static. Static is a big enough problem for balloons that most party decorators, balloon artists, and florists tend to have static guard spray on hand.
I've also had my fair share of personal experience with static destroying balloons. As a looner, I learned pretty quickly that whenever I vacuumed my room, I needed to put all my balloons away (preferably somewhere elevated) and keep them off the floor for at least a few hours afterwards. Any time I got the balloons back out too soon, there would be at least a few spontaneous KABOOMS (sometimes many). I also learned that during the Winter I had to be significantly more careful with my balloons in order to avoid popping them. The combo of carpeting and dry air (from having the heat on) made static buildup a huge problem and often resulted in lots of unwanted pops if I wasn't careful.