Not if it's low enough.
No more tacky than telling someone about your designer clothing, the people you've dated, the fact that you were a cheerleader or football star in HS, or other things nobody really cares about.
Yes, I see no reason for it at all.
Yes, especially because of how uncommon IQ tests actually are and how worthless they are.
Unless you have a specific reason to do so, yes it's tacky.