I guess that depends on if the bell-pusher can hear it or not

Obviously the mechanics of it wouldn't be too hard to implement - a bit of flash memory (how much depending on how many songs you want to store, unless you're accessing them from your computer, in which case that simplifies things but it would need to be on all the time), small wifi card (or even one of the Bluetooth versions, or just use some proprietary stuff in an unlicenced band), minor software and Bob's your uncle.
My only gripe would be a 3+ minute long doorbell - might get on your wick after a while.