Fortunately, those same legal principles in the US cannot be overridden by a treaty.
Unfortunately, the UN mostly works as a venue for governments negotiating with governments, with accredited NGOs having a position of being tolerated in those discussions, but with no real power. Outside of those tolerated NGOs, influence drops even further.
(When I was at EFF, we did try to get UN official accreditation, but China would consistently veto it. There are other digital rights groups that have been accepted though, and we worked very closely with those. The full list of NGOs are here: https://en.wikipedia.org/wiki/List_of_organizations_with_con... )
I think it almost doesn't make sense, in that I perceive EFF to be, whether overtly or not, a very American organization with very American public policy views.