I can't speak to the touch 2 cover but I have an RT device with the touch one cover and I have a surface pro 2 with the type 2 cover and both do as you expect. When folded back, no input, when you open them for typing, they have input.
Every now and then I had to disconnect and reconnect the keyboard to get it to recognize, but not that often. If that doesn't work, something is wrong, maybe look in device manager?