God, as a hypothesis, is not falsifiable, for largely the reasons you point out. Some people pretty well versed in the history of science hold both that Science is, by definition, committed to natural explanations, and can't include supernatural ones, and that God MUST be a supernatural entity. That, though, is a slightly different argument from the one you're presenting. The thing is, we can imagine purely natural aliens, with nothing at all supernatural involved, but they could be impossible in practice to use as a scientific hypothesis to explain anything else.
They could, for example, be individually much smarter than humans. In a simplistic sense, what could we really conclude about what aliens with say, 10 times or 50 times the neurons, or equivalent structures, in their brains (or equivalent structures, again). If they wanted us to believe something was a fact, the overwhelming probability would be they could manipulate us into believing it whether it was true or not. Maybe we could trip up some types of aliens that were somewhat smarter than us in a contradiction, but postulate ones that are smarter by enough, and that chance becomes vanishingly small. There's not any sharp line between unfalsifiable in practice and unfalsifiable in theory, and no real need for infinite knowledge (omnescience) to even be possible, just intelligence somewhat better than human levels. .
Alternately, wouldn't the same apply about aliens that were not all that much, if any, smarter than us, but had millions of years of civilised history, and had been through first contact situations with hundreds of other species before meeting us? Just their having been inventing space travel when we were still working on fire might mean they had enough of an advantage we could never detect what they didn't want us to detect. Or what about aliens who were no smarter than us, and had not been through many first contact situations, but had discovered some new principle that somehow worked better than any form of logic we know. Science can't prove that there is nothing possibly better than the scientific method itself (or it it somehow does, we still can't trust the proof is right). This problem starts kicking in at very low levels of knowing, not just as we consider something omniscent, or nearly so (whatever that last means - isn't any finite amount of knowledge infinitely less than infinite knowledge?). If we encounter aliens that appear to be not much more advanced than we are, or even if we get to them first and they appear backwards, how could we really prove they were? Those simple peasants that aren't resisting being rounded up and executed could conceivably be Organians, after all. How do we prove they aren't?
You've presented a respectable argument for God not being part of the scientific method. I just want to point out that, since it applies to a lot of things we wouldn't call 'God' by any normal standard as well, it's an argument about the limitations of the scientific method itself, not just about whether that 'God' exists.