To call something a State Church in the US really means nothing because there is a formal separation of church and state. It's actually an oxymoron. What you are speaking to is their tax status.
Watchtower is a nonprofit organization which means they do not pay taxes.
It is also a 501c3 organization, which does not necessarily have to be a church, but means that people who donate TO them will have their donations be tax deductible.
Because of the guarantees of freedom of religion recognized in the first amendment to the American Constitution, all religions are given great leeway, some will say way too much leeway. What happened in Norway will not be happening in the US.
This could be why the Governing Body are so shocked over the decisions made in other countries. They have a very American point of view where they have won many court battles in the past.
The idea of the US government taking away their tax status is not realistic.