I can play mp3s when Im downloading. Im not sure of exactly what your setup is.

I use STP
http://systrayplay.chat.ru/

This is a system tray player that can play mp3s and cds. It has an equaliser and lots of options. You need to make sure this software or any other player software is associated with mp3s to ensure it is used to play the files.

I check a download after about 10 - 20 % to make sure the file is one I want to complete downloading.

You may already have a play such as Windows Media Player (yucky), RealAudio player etc than can be used to play your downloaded files.

What do you use to play the files after they have downloaded?