It is possible to transfer a file descriptor to another process, which behaves like a cross process dup(2). See Can I open a socket and pass it to another process in Linux for details. But this needs to be explicitly done, i.e. one process sends the file descriptor and another receives it. Thus the "unrelated" process must cooperate.
But a listen socket cannot be used for monitoring. The socket can only accept a connection but it is not possible to see if another process accepted a connection on the same socket, no matter if the sockets are shared with fork,threading or by file descriptor passing.
Given the right permissions and OS you can monitor the behavior of an application at the syscall level using the ptrace(2) or similar interface. There you could see if the application uses accept and what it returns. Or like suggested in a comment you can use packet capturing (tcpdump, raw sockets) to simply watch the traffic and deduct from a successful TCP handshake that some (unknown) process must have accepted the connection.