I don't own this yet, which is why I'm asking:

Does the GOG release include a bin/cue file for the CD audio? Just want to make sure. I don't see it mentioned on GOG's Blood page.

Sort of. The file game.ins is the cue that references the ,ogg audio files. The file game.gog is the CD image of the data files which include the videos for the cut-scenes and other material.

Could they be renamed to cue and bin files and still work? I'm mostly asking for backup purposes.

I honestly don't know. I haven't tried. If you want to try, you just need to update your dosbox.config files to reflect the name change.