I’m not familiar with Geiger counter design/specs but would the considerable static electricity send some electrons into the detector and cause a false positive beta hit?
Beta particles are basically energetic electrons flying around, yes, but for a Geiger counter to detect them they have to be quite energetic in order to penetrate the Geiger tube itself (detection occurs essentially inside the tube, in the gas)... So I doubt that static field is generating electrons anywhere near that energy needed to be detected by a Geiger tube.