In the recently published ‘Oxford Modern English Grammar’, Bas Aarts classifies pronouns with nouns and not as a separate word class. In this, he follows the authors of ‘The Cambridge Grammar of the English Language’. Is this now a widely accepted practice in pedagogic circles on both sides of the Atlantic?
The answer to your question depends on what you mean by "...classifies pronouns with nouns and not as a separate word class." If you mean that Bas Aarts says that pronouns are a subclass of nouns, then the answer is yes: pronouns are taught and understood to be a type of noun.
If you mean that Aarts does not draw any distinction between pronouns and other nouns, then no, pronouns are still taught and understood to be distinct from other nouns by reason of their anaphoric nature.
If you mean, however, that distinctions are drawn between anaphoric nouns and other nouns, but the name pronoun is not kept (i.e. pronouns as well as all other nouns are called nouns and nothing else), then the answer is no. Anaphoric nouns are still commonly called pronouns.
I'd regard pronouns as a subclass of anaphoric reference.