Yes, were Rockbox to replace it as a default firmware games and UMDs would be completely out.
In theory, for those who have homebrew-capable firmware (or using the TIFF exploit, depending on what is accessible through that, and whether Rockbox can function without the kernel-mode on a PSP) it might be possible to adapt Rockbox to a stand-alone binary for use as an audio player.
Loading the binary isn't really a big problem since PSP homebrew already has a variety of methods for loading one, so the bootloader step can mostly be skipped. Some SDKs have been created for the PSP as well, so really you have a starting point for a port right there, since there's a good deal of hardware information among that I'm sure. In all honesty though, it'd be much more like running a simulator on the device, since Rockbox *is* structured as an actual firmware.