In order for a CD burner to work effectively, it must buffer large amounts of data and be able to stream that data continuously to the burner without any hiccups. That means it must have a lot of RAM and a lot of processing power, something that the empeg has neither of. Also, the IDE controller on the empeg isn't built for speed, I think it would have trouble reading from the hard disk and streaming the data to the CD burner at the same time. On top of that, you'd need to port burner software to ARM and such, since there's no software of that kind on the empeg.

If you're asking, "is it possible to plug in a CD burner and have it magically do things for me without any hard work on my part?", then the answer is a definite no. You'd practically need to write everything yourself and deal with all of the limitations.

If you're asking "is it physically possible to plug a CD burner into the empeg's IDE cable so I can deal with the issues and the programming myself", then yes, as long as you supply your own power to the CD burner and your own IDE adapter cable, and you're a complete genius and can write the software yourself.