I think it is unlikely to work. The “sprint” buttons are simple switches which can be wired directly to the control unit. The Di2 shifter controls use a proprietary communication protocol which is encoded in firmware.
I found this out to my great cost when I tried to integrate the Di2 wiring into a frame by running copper tape between layers of wood and using it to connect the various DI2 bits. The shifter firmware refused to interface with the changed wiring: I am guessing it didn’t receive the correct handshake to enable the protocol. The rear derailleur, however, was OK with copper tape in the chainstay connecting it to the interface box. Go figure.
I ended up having to rebuild the frame with standard internal wiring (except the chainstay).