Very difficult to do. Every aircraft has its own unique ID for the Inmarsat system which the ping addresses and to which the addressed device replies. This is the first stage in the exchange of data to the satellite but MH370 apparently didn't go any further. Any drone would need high speed and range and under this scenario would be sacrificed in the ocean.
The transponder is a different system and can be turned off in the cockpit (I believe). The transponder replies to interrogations from the secondary ground radar and replies with the 4-digit octal code (squawk number) which has been set in the cockpit by the pilots. Depending on the type of transponder other information such as altitude and speed may also be sent. This gives a more accurate reading of altitude than a primary radar would. Back in my day the system was called IFF - Identification Friend or Foe.