No it doesn't. It just means "could god A or god B or god C or . . . exist"?
If your position is "no god that has ever been believed in or that anybody might dream up could possibly exist" then as an atheist, you don't have to define any god to deny its existence. You don't even have to speculate on the characteristics of the unspecified god to deny its existence.
Nope.
Atheism isn't a belief, it is a lack of a particular belief.
An atheist is simply someone who when asked "Which god do you believe in?" Answers "none.
And if the entity you are asking about is not a god that any of the religions claim exist then of course you have to define the god you are talking about.