Yes, it is quite effective in my experience. Most fish will pay so much attention to the fish in the mirror, that they forget to fight with the other real fish...or at least they will split their time, which still benefits.What are the benefits of placing a mirror? Are you saying that the fish will be distracted by their own appearance and thus prevent actual fights between them from happening?
I like to move the mirrors around every day or so, so it appears like that mystery fish is coming from a different direction. Also, some fish will pace so much constantly back and forth across the mirror, that I fear they will wear themselves out...so maybe remove the mirror for a period so they get a rest.