As I explained before, even if Theater is a selection from Infinity Menu, I remember I wasn't able to see my clips from the campaign.
The theater in Halo 4 seems to be worst than it was in Reach. I explain:
In Reach, theater saved automaticaly your previous games and you could watch it when you want with a temporary files save, directly from the theater. Now, you have to go to the main menu, press start, going to file directory, search your clip then save it to view it in the theater.
And when I was doing that sort of thing, there were no campaign clips, only multiplayer, even if I had finish a level from the campaign.
But I think it will be okay for Spartan Ops, 'cause it's from the Infinity.