Could we use image hasing techniques for images classification tasks?
You could, but it won't be very effective.

Image hashing is aimed at detecting two instances of almost the same image.  So, if your training set contains an image of a dog, and the test set contains an almost-identical image, then using image hashing you could use that to learn the label of the test set image.  But in practice that doesn't provide much generalization power.  In practice, we want to take hundreds of different images of dogs, and use that to learn to recognize new images of docs, so that if in the test set we are given a totally new image of a dog, we can still classify it as a dog.  Image hashing won't help with that.

In other words, image hashing isn't designed for this sort of thing and will work poorly.