I guess I was just stuck on the fact that you wanted to bluetooth to the receiver. After looking at it, I don't see why it wouldn't work. I wouldn't say its too cheap to work well, I used to run a sound system at my church, and let me tell you about some cheap wireless mics. Yeah I say give it a shot, and if it doesn't work you are only down 12.50.
EDIT: Of course don't look for stellar sound to come from the mic, but I doubt you want to use it for something that needs to be stellar.