It's possible BUT:
1. Games have their own music, adding such a feature wouldn't kill their music or sound effects. (Pacman and classics excluded, but still)
2. Windows mame version use directx for the sound channels. Depending upon your sound card, playing mame while playing a game will lower the sound quality of one or the other. Also depending upon the media player you are using the eq's of the player and mame can "fight" each other, causing the volume of the song to be either too low or too high.
3. As it's already been said, it wastes resources.
4. The front-end itself should NEVER do this. The main reason being playing a mp3 takes a few resources, but keeping a fe active in the background takes a TON of resources, even on the simplier ones. if you display all the artwork for a game, that's about 5 megs of memory there. Most modern fe's have a memory footprint of at least 10-megs.