In general, no. Science cannot disprove the existence of God. But in my opinion this has less to do with the limits of science and more to do with the extremely broad concept of God. There's no reason to assume that, if a God existed, science categorically wouldn't be able to demonstrate their existence; but even if that were true, we can't assume our inability to do so categorically eliminates the possibility of their existence. God, as a concept, can always slip into the gaps in our knowledge, and even if no gaps existed a God can still exist that is entirely exempt from our ability to understand or comprehend them by any means, scientific or otherwise.