My guess would be that the UN still exists, but for practical purposes little more than a nostalgic dream. The bureaucracy from NY would be hard to move in any reasonable time, and many of the staff there (that didn't transform) would more likely than not be recalled to their various home countries.
The five permanent members of the Security Council (China, Russia, France, UK, and US) all certainly have some form of government (or government-in-exile); the issues I see there would be some contested claims to the right to the UN seat. Aysle doesn't have the social axiom to even try to operate in place of Great Britain, but might have some Core Earthers who view their loyalty to the land more than a particular regime. France would be in a definite fight against Malraux for its seat. The US, though heavily invaded by the Living Land, would face no contest, as nobody in the LL could see the point of the thing. Russia's has no problem - heck, when the UN was conceived, large areas were under enemy occupation, so what else is new?
China under Pan-Pacifica would keep its seat, and might be the only permanent Security Council seat under direct control of a High Lord - though that would be enough to invoke full veto power, which would paralyze the UN from mounting any major military operation. Note also that Russia would wield the veto to block a lot of CE action that would interfere with Tharkhold.
Note that a seat in the UN, even the 5 permanent Security Council seats, do not necessarily reflect contemporary reality of power or position. China's seat was held by Taiwan for years after Mao took over mainland China.
Orrorsh and Nile wouldn't care much - again, lower social axioms would limit the UN's ability to operate as it has in the past, even if the ideal of international cooperation is real to them, though very limited in scope (i.e., Congress of Vienna/League of Nations, methods of limiting war, but not major social agencies). Nile might claim Egypt's (and other nations') seats, and transformed India would have its seat, but more as a matter of prestige than function.
With all that, the UN would function as little more than a veneer for debate, but unable to accomplish much of anything significant in either social or military realms, whether due to lack of bureaucratic infrastructure, or PP veto in the Security Council. I like the idea of Australia being the new base - or maybe the seedbed of whatever organization rises to replace the UN (whether the Delphi Council or something else). (The League of Nations that failed to prevent WW2 wasn't officially disbanded until the end of WW2.)