Yes! The config file option (an example config file is included with the MPD source and an example is in the MPD man page) is "state_file". The state file is specified like: state_file "~/.mpdstate". If a state file is specified, when MPD is killed, the current playlist, current song playing, player state (play, pause, stop), random mode, repeat mode, and crossfade settings will be saved to the state file. When MPD is restarted, it will restore the settings and playlist from the state file.
MPD version 0.11.5 and before Edit
MPD writes the state file when exiting due to the `kill` command, when exiting due to receiving a `TERM` signal [for example by doing `killall mpd`], or when receiving a `HUP` signal
MPD version 0.12.0 and after Edit
MPD writes the state file when exiting from a mpd --kill or using the 'kill' command in the protocol.