I’ve watched a video showcasing the military ward and a seemingly-well communicated group wipe several times.
People will get demoralized after their first wipe–all their buffs will be gone. If one player makes a mistake, such as an early pull or not standing out of LOS for an AOE silence, the raid group will likely wipe.
On top of that frustration, you will have a lot of greed. I can see that the difficulty will not be the fight mechanics alone, but the group’s patience and endurance to stay sane.
There is no doubt that a select few guilds will clear Naxx quickly and make it look easy, but the mass majority of players will face an up-hill, mountainous terrain of strife and agony.