If all the sockets are in use then what ever is calling for another socket, be it Server or UDP should fail to get one.
I vote "no" on that. If you need more sockets, may I suggest the w5200.
edit: As a matter of fact, I was already trying to devise a way to reserve a socket for client communication while running a server.
edit2: After a little thought, it would be fine with me if
socket 0 was reserved for client tcp stuff
socket 1 was reserved for UDP stuff
socket 2 and up for the server. 2 if w5100 or 6 if w5200