My intuition tells me it doesn't work that way, regardless of the complexity. A small rock is also filled with quantum entanglements of unimaginable complexity connected to every part of the Universe. In fact if it were possible, it would nearly prove that we are living in an eternal simulation already so it really wouldn't matter what we "think" we created since we'd just be some other entity's program running who knows where on who knows what "device." God?

Also, it would lead to such a horrific set of ethical problems such as the ability to launch an artificial consciousness into space in a state of perpetual torture and anguish or the ability to mass-produce cloned consciousness on an industrial scale. To what purpose?

As I said, I don't see the advantage as a species unless we can transfer our own singular consciousness to a far superior body perhaps for space travel or a type of immortality. I find it to be more compelling to try to actively avoid seeking to create artificial consciousness and play God when we can see so many benefits without it and few advantages with it.

Incompleteness Theorem is used all the time in machine intelligence philosophy and was born out of computational mathematics.