I got through Greenlight in 6 days, with something like 1k yes-votes and 3,5k unique visitors, and first of all I just want to stress that I did not at all expect it to go that quick.
I had estimated it would take at least a month, or that it would not be possible at all, since the game is pretty strange.
In addition to greenlighting Belladonna I have also attempted, earlier, to create a few items for Dota2, and Valve uses a very similar system for handling submissions for that. There aren't any public details exactly how this system works, but it doesn't seem to be as simple as how many votes you get.
My own personal theory is that you can forget about visitors and votes. What happens is that a product gets "popular" enough that some Valve employee accidentally happens to look at it, and deems it promising.
That might sound a bit dark and cynical, and like I am bitter, but I don't see it as a bad thing. The system which greenlight tries to replace is this: everyone emails their games to Valve, and the people working there accidentally look at some emails and find them promising, and not on others.
I don't think Greenlight is a perfect system. It's a popularity contest, and it doesn't even try and hide that fact. Is it fair? Is it democratic? Can something ever be perfectly fair and perfectly democratic at the same time?
In truth, I have absolutely no idea how and why Belladonna got through Greenlight. Now I have to change all my plans, throw my old to-do lists out the window and adapt to this new situation.