Since BJ won't give his numbers and data I thought I might take a quick swing... So based on a few fairly reasonable assumptions, lets see if diamonds could be self sustaining in GBG...
League - Diamond
Diamond reward rate - 1.9% (0.019 is based on over 12,500 samples)
Cost to diamond buildings - 50 diamonds
Average number of slots/sector - 2
Retention of existing buildings - 50%
Average hold time of sectors - 4 hours
Average value of sectors - 100 (center is worth more, edges less, the only example I could find was an average of 102 victory points across the board)
Victory points gained in season - 300k
So with those numbers we can figure that roughly 37,500 diamonds will be needed by a guild in a given season.
That would average out to 535 diamonds per player in a 70 member guild.
A player that does 5,000 battles would gain approximately 2375 diamonds in the course of a season.
A player that does 2,500 battles would gain approximately 1187 diamonds in the course of a season.
A player that does 1,000 battles would gain approximately 475 diamonds in the course of a season.
In a perfect world, 300,000 victory points should mean 750 sectors acquired, meaning 120,000 battles in a season, and would create a hypothetical maximum of 57,000 diamonds won in a season. But not every sector is going to turn over every 4 hours, leading to less battles and hence less diamonds, both won and spent. Every negotiation further reduces the total number of battles by a factor of 2, and so halves the diamond rewards but doesn't change the diamonds spent. Also, not every guild wins with 300k victory points, some win with more, and many with less. The number changes the diamonds won, but also should require more or less diamonds spent relatively as well.
So from those numbers we see that if every player does 1k battles the guild would be 4,250 diamonds short, and in reality no guild is going to have even a majority of players do 1k battles, so at this level any guild is going to be way short of breaking even with GBG diamonds, and that assumed every player put all their diamonds won back into that GBG season.
If 5 players managed 5k, 10 players managed 2.5k, 25 players managed 1k, and the remainder did 100 battles a season, that would total up to 37,045, still a bit short, but close, and I believe that to be too much at the high end of reality.
So anyways, I thought I'd just throw out some numbers for a seat of the pants calculation that shows that it is potentially possible for GBG to be self sustaining, however the reality is that it is almost certainly not going to be. Play with the numbers if you like, the basics are fairly solid, though there are a lot of factors that could change the outcome substantially in number, though I doubt it would change the overall situation enough to make GBG self sustaining for diamond usage.