I do believe music is absent from the steam version of both Quake I and II and I was wondering if the gog version has the music to both without mods

As for Quake 1, the answer is yes and no. The DOSBox version of the game has the music, while the Windows version had it removed some time ago due to licensing issues. As for Quake 2, I'm not sure, because I haven't played the GOG version yet. I only used the Quake 2 RTX remaster, which imports files from GOG or Steam version of the game. It imported music as well, so there's a high probability that it works in the base Quake 2.

Yes, both games have musics included (only gog version, not steam and bethesda versions)

The last time I installed Quake 1 there was no music in the Windows version (both the GLQuake and WinQuake) . Are you sure that things have changed?

I mean DOS version, not windows

for windows version you can only mount .cue files with a program

GOG provide music for Quake 1. Somewhere in pinned (or not?) topics mentioned that. They remove ogg music but add FULL disk image. For DosBox it mounted automatically (actually that set in many dosbox conf files in game fodler), for Windows you should do it manually.

Quake 2 use ogg music.

I dont believe problem with OGG for Q1 any else except DosBox compatibility. Using DOS and DosBox versions are priority for GOG.