Well, not exactly. Don't get hung up on the christian definition of god, or any specific definition of god.
The answer to the question "could god exist" is most definitely yes, but that isn't the important question. The important question is, as you stated at the start of your post, "does god exist", to which the answer, if you are honest, is, "I don't know". You can add, "but I don't think so", or "but I seriously doubt it", if you want, but in the end you cannot answer the question absolutely one way or the other.
As for the existence of god being a scientific question, I agree that "god exists" is a theory, but I disagree that it presents a scientific question, since god, by definition, can be outside the laws of the physical universe, and thus untestable by the scientific method. If god made the Universe then it must "predate" it, and is therefore not bound by its laws. God, if it exists, may be bound by some laws, but good luck with defining what they might be.
Please answer this simple question - do you know for certain whether or not god exists?
If the answer is no, then you are agnostic.