There's no such thing as UN law. There are treaties between nations, frequently brokered at the UN, and there are UN resolutions, which are more like "this statement was not vetoed by anyone" than they are rulings of law.

Any devolution of ICANN's powers to the UN (which, if not massively fucked up, is probably healthier for the internet than keeping it under one country) would likely be an administrative handover. I seriously doubt it would be done on the basis that the G77 voting as a block could take control of the net.

For an analogy, look at the way the UN peacekeepers typically handle things. They go someplace where there's peacekeeping.. and then they sit there. They don't do anything and avoid taking a side at all costs. If either side says they're not welcome anymore, they're gone.

The UN isn't a government, it's a really big conference room.