Is it possible? I really like the idea of not having my music stop when restarting X and stuff like that.

It's not currently possible.
While I like the concept of mpd, it does a lot more than just play songs, it handle the database for example, which would severely limit what gmusicbrowser could do if gmusicbrowser where to use mpd.

If it is just so that the music keeps on playing when gmusicbrowser is not running, I guess it would be possible to send the current playlist to mpd, but it would requires some significant changes, in particular with the random modes, that currently pick the next song at the last moment. And the only benefit would be running temporarily without X which is not usually a big problem for users I think.
So I don't think I will implement it.

What i would really like about the idea is to use mpds good features like crossfading.
When gmusicbrowser would manage the complete music handling but only give mpd the next song to play, and mpd is then doing the playback, i would like that concept alot.

Only my thoughts here :D