I'm going to install the game to my HDD but if the third disc is just for MP, then I will only install the first two, as MP doesn't interest me?

As far as I can tell, I have only been using it for multiplayer. I am not that far in the mission.

Yes disc three is multiplayer only but try out wasteland legends co-op its pretty sweet. You should be fine just installing the first 2 discs.