Yes. God (according to my beliefs at least) exists independently of His perception in the feeble human mind. God Almighty is so much more powerful, strong, and vast literally all-incompassing, that it is truly impossible for the human mind to come even close to truly understanding his greatness. Men and women over the years have come close, Muhammad, Jesus, Moses, Abraham etc. being the best examples I can think of, but no human being I believe has the capacity to truly and fully understand the totality of God Almighty. Now if it were possible that God gave a human being this power for even a second would it be possible, that is a very charged metaphysical question and I cannot answer it. The religious person would say, yes, of course it is possible right? God can do any thing he wants right? Well, can God create three more gods? How about four or five or six or seven? Can God create a burrito so potent and spicy that even He dare not eat it? :p

Anyways, yes, God exists whether the whole of humanity believes in him or not a single, solitary soul. It's awfully arrogant (in my opinion) for us to think that God would stop existing if we rejected him or stopped believing in him.