Shit, when I watched the quick look I was worried, because while installing usually does help, it's usually not THAT big of a difference. But when I played it, it was just a ridiculous difference. In the quicklook Jeff waited on the disguised load screen area of the Normandy for a long ass time, and when the game is installed it's almost instant. And the armor shit wouldn't even load in the quicklook, and while installed it's almost instant for me.
So yeah. You should probably install the game if you have the space.