This sounds like a great idea. There is one small problem with playing a drum machine thru your amp. If you don't have a tweeter or horn for the higher freq. (like the cymbals) no drum machine will sound good. This is no fault to the BeatBuddy of course or any drum machine.
A 'beats only' balanced out (TRS) jack would solve this. Just run it to an amplified PA speaker (or the mixing board) and you're good to go onstage.
um... David, if you use this idea, can I get a discount?...