process buffer passed to log function for network processes?

[Juanma Barranquero]

Emacs Lisp Reference, "37.15 Network Servers" says:

   * If the server's filter is non-`nil', the connection process does
     not get a separate process buffer; otherwise, Emacs creates a new
     buffer for the purpose.  The buffer name is the server's buffer
     name or process name, concatenated with the client identification
     string.

     The server's process buffer value is never used directly by Emacs,
     but it is passed to the log function, which can log connections by
     inserting text there.

Which log function? Docstring for `make-network-process' says:

    :log LOG
          Initialize the log function of a server process to LOG.  The
          log function is called each time the server accepts a network
          connection from a client.  The arguments passed to the log
          function are SERVER, CONNECTION, and MESSAGE, where SERVER is
          the server process, CONNECTION is the new process for the
          connection, and MESSAGE is a string describing what has
          happened.

A server *process* is passed.

Related question: Is there any way to associate a log function to a
process after it is created? Apparently, no.

    Juanma