For me, backing up my music files is equally about not losing my music as not having to re-feed all of those CD's into my computer (I have over 1000 CD's digitized), so this would not be a good solution.
Also, (although I know, for you, it is a moot point now) fireproof is not fireproof. The box gets rated for a certain duration at a certain temperature, you don't have much way of knowing what temp and duration you might actually encounter. Usually people are concerned about papers igniting, but I would be careful about believing plastic CD's would not melt if the box is exposed to continued high temperature.
Poly carbonate gets soft (will warp if under load) at 297 F and actually melts/flows at 311 F and paper ignites (of course...if you are familiar with Ray Bradbury
) at Fahrenheit 451!