Yeah, I definitely think it should be optional. I wouldnt want to play a single player game like that. But say I long ran out of HDD space, had to delete COD: Ghosts, but I get a random message from an old friend who wants to play right now. I'm far from concerned about the graphics at that point, I just want it up and running ASAP.
Ideally they'd have some sort of progress bar that tells you exactly whats going on. So saying we're talking about an MP game, it starts pure red and it says unplayable. Then it turns to orange and says "limited map selection, low quality" - but at least its playable at this point, and it continues to DL map by map at low quality. Then it turns yellow and says "Some maps low quality"....eventually it turns full green when full detail is available for all maps.
I think that would suit everyone as long as its clear what you're getting. Maybe they could put another option to prioritize quality vs. getting you up and running sooner.