I think it is very possible. I would suggest you start a new thread.
Off hand I can think of two options (I'm sure there are many more)
A Qubino Flush 1D Relay. This is a 120V device however so it could be used in two configurations:
- to operate a 120V relay whose contacts enable/disable the doorbell
- to enable/disable 120V going to the door bell transformer.
John