Yes I have used Lego Rock Band, Rock Band 2, GH III, GH5, and GH World Tour all with the Band Hero Wii instruments with no problems. You will have to calibrate with each individual game the first time you play each but it is not difficult. (I do not have the Beatles but I've heard it also works with this bundle)
It's just a function in options to sync your instruments with your TV. I hope your son gets as much enjoyment and stress relief from the game as I do. Make sure when you buy the new games you are careful to buy them for the correct system, it can get confusing when they are all offered from the same screen.