As an example, I read three books online, would the counter 冊 still be used? I know that counters are based on size and shape of physical items, do the same rules apply when reading a book online?
counters are based on size and shape of physical items
I'm not sure what you mean by this, but not really --- I'd say we choose counters based upon what we perceive the object to be.
So, for ebooks (as in Kindle), 冊 is used. When you see an object in immersive VR, corresponding counter for that object in real world is used. (On the other hand, developers of the VR might count them with '個' when they consider them as object that needs to be rendered, rather than what they represent.)
For e-books, things can get a little complicated. When you read three articles on wikibooks, I don't think 冊 is appropriate because they are more like online documents rather than books. Documents that are built to be books, on the other hand (like Learn You a Haskell for Great Good!), I'd use 冊. I feel that PDF documents and EPUB documents are more likely to be considered as books in this sense because of how they are styled. Anyway, although the exact line between online documents and books can depend on the writers' preferences, I think those meant to be books can be counted with 冊.
(Edit: This is my personal observation, but I feel that the essence of the counter of 冊 is pages [not necessarily in physical form]. E.g. 巻物 are not counted with 冊. Thus some e-books without the concept less likely matches 冊.)