If you wear you "I Voted!" sticker and fight the resulting monster, but then hit it with a macrometeorite (I did this to get a lobsterfrogman), the _voteFreeFights variable remains what it was before the fight. However, I can confirm that the actual number of free fights does get used up this way. I had two fights normally, did the macrometeorite trick on a third, and then fought a fourth normally, and that fourth one cost me an adventure.