Yes, as mentioned the key is to set up mpd through ALSA. Most distributions will be using pulseaudio as their main sound mixer. You need to bypass that, and pump your music out directly via ALSA. mpd is probably the most popular music server, as it's unobtrusive, flexible and is happy interacting directly with ALSA. I think all cell phone operating systems have good cheap applications that interact directly with mpd.
Any linux distribution will let you do this. Depending on the distribution you choose there will be slightly different issues.
I run a headless linux server, i.e. the computer has no monitor or keyboard connected to it. Basically it's a computer with no moving parts, that's tucked away where nobody notices it. The advantages is it's minimalist. The downside is it's a bit of work to perform major software updates -- most can be done by wifi, but occasionally you need a monitor and keyboard for direct access. That's why I prefer distributions with little overhead and infrequent updates.