This would actually be a lot of fun to watch, IMO. I correctly predicted Rag would die under a week, but even the best players in the world can't roll in to Naxx toting greens and blues and expect Patchwerk and Loatheb to fall over.
It would still probably happen absurdly quickly through insane grinding of reputation (Zandalar, Cenarion Circle, Brood of Nozdormu, Argent Dawn, plus tier 0.5 would be available). I guess the question becomes can AQ40 be cleared in ZG and AQ20 gear, which I have a hunch the best players in the world min/maxing an ideal raid comp certainly could.
So even though I don't think C'thun would make it 14 days, I still don't see Loatheb or 4H falling over until they have 2-3 full clears of AQ40, 4-5 Onyxia clears, and 8-9 ZG and AQ20 clears.
Although the faster it opens, the more luck matters in drops too. Actually it also makes a big difference if BWL can be cleared in the first reset. I'm guessing it could be because warriors do so well on Vael but it'd also be interesting because if a player lost their Onyxia buff there'd literally be no one else on the server that could provide it.
That first reset is super critical. I'm not sure if people can level fast enough without layer hopping or that bug that let them get full experience in a raid. There's just so much to do in that first week, because someone has to get Hydraxian rep, someone has to get the UBRS key, someone has to level leatherworking for the cloaks, they wouldn't be able to get 500 Hand of Justices and Savage Gladiator Chain, etc.
I also don't know how much of a problem frost resist gear is in Naxx, do people even wear it or is it just potions + insanely high dps now?
Assumptions:
--The guild has the server to itself for the first week, therefore it's easy to level, get black lotus, and get world dragons but they must make all their own arcanite and mooncloth, farm up the recipes for flasks, provide their own onyxia head buffs, get their own edgemaster's, etc.
--No multi-boxing
--No layering
--No bug with the raid group getting full xp
I think it's hard enough that the winning strategy would involve doing splits. But it'd be interesting to see if the winning team would choose to, say, farm Hand of Justice first or immediately work on alts to get a split done in the second reset. Because anything that Naxx trash drops could also be farmed, which might be better than splits.
This would be a lot of fun to watch but to do it responsibly Blizzard would probably have to shut the server down for 12 hours / day or something.