I honestly doubt that enough people will bother min/maxing their garrisons enough to empty out the capital cities. There might be a noticeable drop from the people that do, though.
Keep in mind that the average player probably doesn't even know a thing about garrisons except that they exist. Just look at how many people on here, a fansite (of which the userbase is generally more knowledgable than the average player) didn't know that garrisons can have an AH. I don't think that the average player is going to a) know about it or b) bother doing the quest to unlock it.