If "a being with unlimited power that does not wish to reveal itself existed" could there exist any evidence to convince you that a being with unlimited power that does not wish to reveal itself existed?
No. Likewise, if that green alien hiding in my closet chooses to remain hiding there, I'm not going to have any way of knowing if it's there or not. I'm not going to start believing in a god or in a green alien "just in case." That's madness. In that case I wouldn't be able to open the door because there "might" be a thermonuclear device triggered by my action. Nothing would make sense anymore if I discarded the need for evidence-based beliefs -- it would be the same as discarding rationality and logic itself.
You assert that it "can never be rational is to take a position without any supporting evidence". I agree when evidence necessarily exists. However I would be hard pressed to agree in cases where evidence necessarily does not exist. In cases where no evidence can exist for any position including the null position, I see no reason to take any position over another nor to avoid any position in favor of another.
No, no, no. The null position, by definition, is what it is most rational to assume without any evidence.
If someone gives you a pill and says "This pill cures cancer." You might be excited. But suppose you were to ask about how he knew this, about what kind of testing he'd done, and he told you that tests don't work on this medicine. He claims that the medicine only works when it is not being tested. If you take the pill, you must not inform others that you took it, and you must never let him find out whether your cancer was cured. If either of these conditions are violated, the pill won't work. No evidence can exist proving him wrong. Would you hold out much hope that this unusual pill would work?
Probably not. More likely, you'd accuse him of making something up so that he could sell pills without ever having to worry about being exposed as a fraud...sound familiar? Anyone can make something up that's immune to testability, but that doesn't make it rational to believe in it. I sure wouldn't buy that pill, and I have at least as much reason to believe that belief in gods is something that people made up.