Actually, we have court judgements that say, any theory that posits a creator is not science by definition.
This happened in a case with respect to ID. As you said, even though they don’t mention a creator directly, and stick tot he idea of a designer, it was concluded that it was not science as the idea was too close to creationism.
So yes, Science suppresses all hypothesis connected to a creator/the possibility of the supernatural within its field of influence by its very nature.