It's almost guaranteed that he did. He kept applying for the DADA position so he obviously wanted to teach it over potions. It wouldn't surprise me if he'd crammed his DADA book full of notes and corrections first before moving on to the potions book. And unlike the potions book, I bet he didn't leave his DADA book laying around forgotten in any old cupboard.

I actually don't think it had much to do with his fascination with the subject (as far has having notes goes); he just struck me as the type of student who wrote notes all over everything.

Yes he was interested and even made his own spells i think he thought he was better then the books at some point.

I always wondered if the book was something he and Lily both shared, a way he could impress her, also a something as a muggleborn that would be easily understood by Lily.
I can't see him having a DADA book for those first years before breaking with Lily, or those years after that.