Apparently at Caltech they had a cheap accelerator, but they got great results, because the physicists knew it inside out and tinkered on a daily basis.
I did spend a year doing what Id describe as 'guerrilla white-board driven architecture' where we basically argued hammer and tong for three hours a day, putting ideas up and tearing them down. So every module and code interface was nutted out in detail and usually simplified. It seemed to keep a team of 12 developers focussed on building the same thing. A smaller wb was used to keep a simple list of what the teams working on. Backed up by an open Plone intranet this brought us to delivery. Probably more suited to medium size teams as in game dev. Part of the success was having done a prototype beforehand.
Whenever I see a w/b covered in those cute little pink and green post-it notes, my reaction is that they are embracing agile too rigidly - that the focus is 'process' not action. Its not a white board if theres nowhere to write, right?
So I think the main benefit is simply that the board, being blank, beckons you to draw whatever idea is bouncing around, which you then have to explain...