I don't think it always needs a question mark, but who knows. In the previous sentence, it is a rhetorical question at the end of a statement.

I was thinking it wasn't needed there, where it would if I were saying something like, "I am not, but are you?"

It's similar but the question is not rhetorical. It doesn't feel right either way now. Is there some other mark we can use? What is that upside down question mark for? That could work.