We're fond of the fact that we exist; that's why we insist God does the same thing. But no-one has ever explained to me why 'existence' would be a good thing for God to have? If somebody sincerely believes God has fingers, eyes and a white beard, we tend to think of them as naif rather than blasphemous; but maybe we should crack down harder on such anthropomorphising of God -- and the claim that God 'exists' is surely the worst offender in this regard.
I suppose the point is that we tacitly assume that saying 'Existence is not relevant to God' (a way, I suppose, of saying 'God does not exist') is consigning God to a kind of bleak after-lifel it is disempowering Him, making Him as sort of shade. But this is foolish. Existence has many valences; everybody is perfectly comfortable distinguishing between 'Barack Obama exists' and 'Napoleon Bonaparte existed once, but no longer exists' and 'Sherlock Holmes never existed, except, in a funny sort of way he does'; and professional philosophers write whole books on the difference between the existent and the ontic, Dasein and Dooby-dooby-doo. Why shouldn't non-existence have a similar spread of valences and possibilities?
The obvious retort is something along the lines of 'I can't imagine how that could be'; but this is only to concede that it passeth our understanding (something traditionally spoken of God as a point of praise and majesty!) Of course we can't think outside existence; its the sea we swim, fish-like, in. But the fact that we can't think outside it really is neither here nor there where the possibility of Divinity is concerned.