Regardless of whether they do, the tech that underlies modern image classification approaches (i.e. deep neural networks) is pathologically hard to understand to the point where it's practically impossible to provide the guarantees you're describing. For example, adding noise to a picture of a panda can make a network think it's a gibbon: https://towardsdatascience.com/breaking-neural-networks-with...

That's not to say, of course, that there's nothing to be done. People who aren't white have historically been laughably underrepresented in computer vision datasets, and while that's been changing, I gather that representation still isn't where it needs to be.