I could swear we discussed the UN in an earlier thread but for the life of me I can't find it!
I
think there were a few options put forward for where it as an organisation might relocate to. Switzerland, France, and Australia were put forward as options I think.
Although the books indicate the UN basically fell apart, it's my opinion it simply lost relevancy and influence as conditions throughout the world grew worse. The
entity itself may have lost a few members and certainly have been ignored on an increasing level, but I can't see any country simply withdrawing completely and not paying at least lip service to it (what's it really cost to have a representative or two in attendance?).
With the US entry into the war, pressure may have increased to move the UN's HQ to a neutral state - France, Switzerland and Australia (amongst others) would seem ideal. France and Switzerland however would loose most of their appeal once nukes began to be used - nobody wants to be around when there's the possibility of fallout. The UN may have relocated again, or for the first time to the southern hemisphere (can't think of any northern hemisphere countries which would have been perceived as safe).