Not in general. You can't detect this watermark without access to the original model (the paper authors bill this as a feature). So the model owner could do tha

Not in general. You can't detect this watermark without access to the original model (the paper authors bill this as a feature). So the model owner could do that test to check if their particular model produced some image, but a third party trying to work out whether a given image was fake (a) would not have the data they need, and (b) even if they did, would need to repeat the test for every possible image generating model in existence.