The morphology of neurons is involved in information processing, I don't doubt that at all. It's also involved in staying alive, and staying healthy, and 'being part of the organism', and a great many other things.
It is not at all clear which specific aspects of the morphology are 'for' processing information we care about in the context of intelligence (because again, even info processing can be 'for' things like making sure you breathe reliably).