Can you imagine why and how any of those powers -- or any of the others -- would agree to anything else?
If the security council can agree on a policy how to represent Earth, they have armed might to back it up.
If they do not, all the bets are off, but I suspect that most of the powers and many smaller countries would do their utmost to fight down any independent movement claiming to represent the Earth their governments do not approve of.
The UN is a bloated thing of corruption, but so is most of all of the organized humanity on any scale, so that's quite fitting. Most of our existing international operational frameworks both de jure and de facto are coordinated under the UN or very related organizations. Assuming the world will resemble the one we live in now, if a need to represent the Earth arises (like, say, alien contact) and if everyone who matters agrees how to deal with the aliens, they'll probably just stick the UN sticker on that decision. If they do not, sucks for us.
If someone not-UN will start their space adventure to find aliens, they'll use their own nationalist / corporate / ideological symbolism. If they in addition claim to represent the Earth or the Humanity instead of just themselves without everyone's approval (can't see that happening, I doubt the permanent members would agree precisely because the reasons you outlined), they will probably have a war at their hands at home. In that case and without drastic changes in the international political reality, I'd wager that the ones who can make their claim to stick would be the UN permanent council members, because that's how they got in there in the first place.