Are mouth plates effective in treating tmj?

Yes. Often, yes. Not always. Make sure you are being treated by a TMJ expert.
Maybe. Tmj is a group of disorders related to the jaw joint and not a diagnosis. There are multiple causes of "tmj" from muscles, ligaments, tendons, nerves, or even tumors. The most effective treatment may be not be a mouthguard. Furthermore, there are many types of mouth guards and they do different things. One kind can make certain conditions better and other conditions worse.
Yes. Bite plates can be very helpful. They must be properly designed and adjusted to a neuromuscularly balanced and physiologic position. They are both diagnostic and therapeutic.
Maybe. Only way to know is to try it. But don't give up after only one treatment. And i would also get more than one opinion before jumping into expensive therapies before other options are tried.