Controlling 'mpd' via socket does not mean that you don't need a client any more, or that 'mpd' takes the role of a client itself. It's just another communications mechanism between the server and the client (which does not need to be 'mpc' of course).
The socket does not exist by itself, you can create it with following commands:
# mkdir /home/tc/.mpd/
# mkfifo /home/tc/.mpd/socket
You can verify the effect after having modified 'mpd.conf' and restarted 'mpd' using command 'netstat -an|grep LISTEN'. There won't be a LISTENING port on the address/port as before (something like: 0 0.0.0.0:6600) but now there will be a socket (something like: LISTENING 99401 /home/tc/.mpd/socket).
After pointing 'mpc' to use the socket via variable MPD_HOST you can then control the server via, for example: mpc add file.mp3, mpc play,.