I couldn't get a reading. I rubbed my bronze watch feverishly on everything I could find around the house that's made of a material above bronze in the triboelectric series. My wife drew the line at me rubbing my watch on her hair, so I used the cat instead (fortunately, he's a nihilist and cares about nothing) but to no avail.
In theory, there should be an exchange of electrons and a resulting charge but if there is, it's so small that it doesn't register on my crude device. I'll borrow an electrostatic voltmeter at my university sometime soon to check. So in any case, there doesn't seem to be a substantial charge, so my hypothesis that it could affect the movement seems less plausible now.
