The only reaction my dog ever had to a mirror was to think to himself, "Man, I am almost shockingly good looking."
I'd let it work, at least a little, because its a creative idea. How well it worked would be dependent on the level of the spell. A Silent Image would probably delay the rats one round, a Minor Image would cause the swarm to disperse and take a few rounds to form back up, and a Major Image would probably cause them to split up, run and not look back.
Actually, now that I think about it, an illusion of snakes might be even more effective. Last winter I had some field mice move into my basement and get into the walls... that was a job. But one of the things the pest control guy suggested to prevent a reoccurrance was to put rubber snakes behind the walls. Maybe that guy was a lunatic, rodent pyschological warfare is not my area of expertise, but apparently even the appearance of a predator is enough to keep animals away. I mean, if you think about it, the ones that were like, "Hey, that looks like a snake. Let's see what it smells/sounds/reacts to stimuli like!" probably weren't in the gene pool long enough to have an effect on behavior.
(In the end I decided against the rubber snakes to go with a more conventional approach. It wasn't so much that I thought it wouldn't work, but I figured a few years from now I'd be doing some drywall work or something and a rubber snake would pop out and I'd either hurt or soil myself. If I was going to put something behind the walls to scare rodents, I was thinking of using some toy sharks. I mean, that's nature's most perfect killing machine, rats would have to be terrified of those.)