A:
Ron
If your medical device is critical to health, I suggest contacting the maker of the device for their advice. Anyone else, like me, might give you incorrect advice that fails to serve your needs.
I wonder whether your medical device has a line-in socket and a line-out socket. If yes, this will probably serve you. Your description has the medical device connected between the incoming phone line and the telephone handset. If there’s no line-out socket, and If you need the phone to serve only for voice communication, then you may only need a line splitter to plug into the wall jack to connect both devices to the same jack through the splitter.
Some comments about this phone:
It does not use AC or DC power; it functions on the energy from the phone line. It has a memory storage capability that requires AA batteries, but does not need them to serve as a phone.
It does not have an internal splitter - a socket for incoming line (from wall or other device) and outgoing (to another device).
This telephone comes with a cable that connects in the back (bottom) of the base, the other end plugs into the phone jack on the wall of your room. The phone handset is connected by coiled cable that you see in the product photo to the base. Everything is hardwired (connected by wire, not wireless), It can be used in table-top mode or wall-mounted. Based on my experience, everything you need is in the box, except for batteries and tools if needed to mount the base on a wall.