Apparently, your notion might be corrected, based on applications the distributions are varied, but theoretically it applies that classifiers' performances are depended on data distribution ( e.g. Gaussian or non-Gaussian). You should also consider this example, a classifier is learned to identify dog face. But, somehow it has been given to test a human with same dog face mask. So, the classifier will still identify the human as a dog, though both of them are different. But, an intelligent system can not do that.