Yes, if the local circumstances will support a good static buildup. In most climates it may be tricky.  Static sparks are quite enough to kill tiny creatures, especially if they are on conductive surfaces that can conduct away the electricity through their bodies.  A more powerful spark can kill a grounded housefly for example.

The old AM radio aerials could give quite powerful shocks that would kill fair-sized insects like blowflies.  I did not continue my researches long enough to give you a definitive list and analysis though; sorry!  :-)

I once was shown that such an aerial wire could actually light a light bulb from ambient fields, so WATCH OUT HOW YOU PLAY WITH SUCH TOYS!

Jon