In a word, no.

The whole idea is based on the assumption that the American system is ideal or at least the best available which I don't believe is true, but I have no idea which system is.

Yes Washington would be the capital but as you said every nation or state as it were would get 2 senators and the same proportion as our current states in the house. Since the constitution only says that the president for instance must be born in the US anyone in the world could be preisdent. It certainly would be a huge improvement over what we have now.
Why Washington? I would say that there are cities with a far better claim to capital. Also would that mean that the US would only have 2 senators? And what would this new super state be called? United States by any chance?

I think the only chance we have of being a united planet is when we find someone, or something, else to fight. That being said the idea of an united planet is a good thing, but unworkable at present.

Most of the world would be much better off if they got the same benefits as US states do. Imagine what a boon that would be for Africa and parts of Asia, it would bring them into the 21st century.

I certainly wouldnt give them a place in congress though..
Oh, so, you want to rule them without giving them their say, anyone for a dictatorship?