Yes it does, but not for the reasons you apparently think.
The debating society you laud isn't what the UN is all about nor is it the danger Ms. Schlafley cites (although if Saddam completes a WOD and smuggles it out of the country while Kofi sweetheart dithers, you will start to realize how dangerous an organization it is). Her concern is multilateral treaties that become supreme law of the land and then have managing secretariats of paid activists that define their terms and applications AFTER ratification. If you want to know where many of the property rights abuses pursuant to the Endangered Species Act or Clean Water Act originated (that have harmed both humans and nature), you need look no further than the UN. UN bureaucrats are now publishing documents specifying land use in the US, the manner of our children's education, gay rights, abortion rights, rights of "migratory peoples"...
You clearly have a lot to learn about the UN. Its true purpose is racketeering and organized crime at the expense of your rights and liberties. Best you had get started with your education.
But at first blush, I'll say that "soveriegnty" doesn't mean the unbridled right of the might to run roughshod over the wishes and best interests of the other people on this planet. But maybe I'm too idealistic.