I understand your original question/statement as valid, but I don't believe the information it would acquire would be of any much use to town, compared to how much use it could be to the mafia.
As town, say that we know me you and Jonnas don't have a role, what does that provide for any of us or the rest of the town? Nobody has even answered your original question on it either, btw.
As mafia though, what does it provide? Potential targets/not targets! I think it's much more valuable information for mafia than town. It's wholly possible at least one mafia member doesn't have a role, and if you're in the mafia you'd know this more certainly, and then go fishing to see who else is in the same boat and therefore not much of a threat powerwise.
So hence, I vote for you. I don't think you'd be stupid enough to do it on the first day, I think you'd be smart enough to do it and pretend you wouldn't be stupid enough.