I would think it would have the opposite effect. Every time you give the player a set of choices, it increases the number of permutations needed in the dialogue tree. If other companions interjected their own responses instead of the player being responsible for every single response, it would reduce the number of player choices, thereby reducing the number of permutations, and thus reducing the required game resources.
Or to put it another way, rather than having to pull each piece of exposition out of each NPC with a game of 20 questions, the exposition could be delivered in a streamlined manner with a few well-directed cinematic dialogue sequences that incorporated multiple characters.
For myself, I would rather have fewer choices, but have each choice be a meaningful part of a well-constructed dialogue than to have lots of choices that all feel like I am just exhausting each NPC's dialogue tree one by one.
