I don't think it is logical to conclude that something does not exist merely because evidence has not been presented. Indeed, the search for discovery of any kind would be made meaningless if all undiscovered things were unlikely to exist.
I agree that the workings of the natural world can be explained without God. Just as I agree a knowledge of the origin and inventor of the bicycle is completely unnecessary to understanding its operation. That said, such knowledge may be illuminating and engaging, may lead to further discovery, may allow one to appreciate the essence of discoveries related to the bicycle's operation in a new way. I do not agree that the assumption of God complicates the natural world, if only because we have no conception of how God exists or how God works. It only becomes more complex when humans attempt to assume how God may have worked, or what his properties are using their own currently understood conceptions of matter and energy. How can someone say something is complex what they don't know what it is? Some pantheistic conceptions of God by definition can't be anymore or less complex than nature themselves because God is synonymous with nature in those conceptions. I make few assumptions about the nature God, much less than many of my coreligionists. I'm uncomfortable even speaking in terms of God the "creator", because the nature of creation and existence is contentious and ill-defined. I don't know if creation means "emanates from, invented by, or necessary to" or any other concept we can come up with.
Inserting an unknown into a theory does complicate it, and makes the theory incorrect.
The natural world is not a theory. There are theories about the operations of the natural world. If God acted upon the universe in a physical way than in one sense he can be said to have complicated those theories, although it would not make them incorrect, merely inadequate. Much in the same way that new observable data did not make Newtonian physics "incorrect," merely inadequate. Further, whether it "complicated" the theory depends on the meaning of "complicated." If it means simply having more elements, yes it is more complicated. However, if those elements can be said to be more harmonious, then it can be said that the system is more elegant and therefore involves fewer complications, and thus is less complicated.
That said, I again object to the entire premise of wanting to bring God around to a physical understanding when I am not claiming such an understanding. I am not inserting God into the operations of the natural world, that implies an assumption about the nature of God.