There's no question Neil can play by ear. We've all heard him do it in concert over and over. In Vancouver last July he played "Something" by George Harrison at the drop of a hat. He botched a couple of chords but noodled around until he found them. He was certainly playing by ear. Elephant ears!
As for whether he writes and reads notation . . . my guess is that he doesn't write out all of the parts. If memory serves some third party scores the string parts on Crowded House albums. You'd think if Neil could do it, he would.
My two cents.