I think it would be cool if it was a rat.
That would be funny as hell, but I'm not sure it would get people to report more posts which I think is Theymos's point here. It'd be even funnier if a rat king image was used for maybe the top 10% of reporters.
Anyway, this is a badge I'd proudly wear, but I report posts basically because it lets me feel like I've done something concrete about the spam problem. It matters less to me that something may or may not get done with my reports. Doing something is usually better than doing nothing, and I think more people should be reporting shitposters and assorted rule-breakers. If it takes a badge to motivate them, go for it.