I have suddenly found myself involved with two completely independent GTD departmental roll-outs at the moment. Both of them are cases where a senior manager got big benefits from using the method on his own workflow and then naturally wanted to obtain the same effectiveness hike across his whole department.
So I have needed to do some hard thinking about
(1) how can you spread the message out to a group in an efficient and convincing manner?
(2) how does GTD effect how people work together?
For the first, I flatter myself that I have an effective presentation that, with management backing, will kick-start adoption. That works because it gives people enough energy to pick up a couple of good habits and I back it up with individual coaching. You do always have to be careful not to push too hard: that can make people feel that they are being criticised as having a sloppy, ineffective way of working...
I can sympathise with them, as I currently look back at pre-GTD-me and grieve for all the wasted energy, drained self-esteem and missed opportunities. GTD has saved my bacon lots of times and I am still learning new things, refining habits and sharpening my game. David Allen himself always puts it nicely in context: if you pick up any of the GTD practices it will put you way ahead of most of the planet.
As to how GTD plays in groups? My take on that is that you will always see increased effectiveness in anyone who delegates, because they track everything they hand off. and all their reports will need to raise their game to keep up: they will at least need to get clear about every project that has been passed to them and what they are doing about it.
There is a US general I read about a while back who uses GTD in his command exactly that way. He runs his weekly review on Fridays, following it up with a staff-meeting in which he checks the status of all his delegated projects. That forces all his subordinates to run their weekly reviews on Thursday, or be "ambushed" when the general checks in on every single project he placed with them...