This seems like a great way to reduce critical communication amongst staff. Will people be willing to ask "dumb" questions in such an environment? Will people be able to communicate freely without having to worry about how that communication will be perceived by those not a party to the communication? Etc. I doubt it.
It seems to me that the natural consequence of this sort of thing is the reduction of honest and frank communication. Or perhaps more likely, in the vein of "routing around damage", people will stop using internal communication tools as much and go to communicating some things solely in person or through communications channels not connected to their employer.