No, it is not fast enough.
Sharp-eyed readers will have noted another event that occurred in 1997. The Arabs are simply unable to focus on a single goal. They have been steadily building spaceship parts, whenever they weren't denouncing the Chinese or fighting a war with them. I am safely allied with all 16 city-states, and have more than 20,000 gold pieces to ensure that I stay allied with them. So, I am the only civilization that can possibly win diplomatically. And yet, the Arabs decided to go ahead and construct the United Nations. Why? Why? Aren't they supposed to be trying to win, and not force someone else to win?
I could, of course, declare war on enough of my long-time city-state allies to prevent myself from winning diplomatically. But I don't, and so, inexorably, unavoidably, inevitably, the UN vote comes to pass in 2006.
And I sadly accept the congratulations for a diplomatic victory.
Actually, I think I did quite well diplomatically. I manipulated two civilizations into fighting wars on my behalf. Each war prevented someone else from winning the game. And during those wars, even though I was supplying troops to one side, I remained on good terms with the other side. (Persia even went to "friendly" status during the Siamese-Persian war!)
Eight years later, in 2014, I completed the utopia project. Persia had been eliminated by Siam, and so could not get its own cultural victory. Arabia had not completed any more parts for its spaceship. I would have gotten a cultural victory -- if only the Arabs had not forced me to take the diplomatic victory that I didn't want.