Sure. Install an ntpd server somewhere (or find one that you can use) and use ntp on all your boxes. This ensures that you have the same time on all your machines. Then use at (as long as you don't have much else running on the machines) or NQS (http://sourceforge.net/cvs/?group_id=17238)--source only I'm afraid--to schedule whatever process you want to use to play the MP3.
Also check out http://www.csse.monash.edu.au/~jon/bqs.html for a list of more batch processing systems. Andrew.