My assumption is NO. For a start, to access the DSTwo real time menu, an interrupt is hacked into a game which checks for a button combination, once it is detected I am assuming that the DS RAM is backed up (save-state) the DSTwo menu is loaded, you do whatever it is you want, then the DS RAM is loaded back and you're in your game again.
When playing a DS game, the system is running a DS game, that game has full control over the ARM7 chip (used for sound among other things) and would need to be hacked to allow the DSTwo access.
If someone was willing to hack the standard DS ARM7 binaries to read and play MP3 files while still playing a game, then there would be no need to use a DSTwo to do so as it would be just as possible without it.
The reason it can be done on the PSP is because the PSP is running an actual OS in the background and it is the OS that is hacked and not every single game that is played.
Also, playing an MP3 would also remove all sound from the game, both BGM and SFX, I for one quite enjoy SFX in games, they make the experience much more enjoyable.
If you want to listen to music while playing a game, I suggest turning down the volume on your DS and using your personal MP3 player.