I'm working on a project in a very similar space, and we decided to add gamification. We don't want to harass our users or annoy them into using the app, and therefore our notifications will be easily manageable. But we believe that gamification is very helpful for encouraging users to learn consistently, and so we will include it. But at the same time, we are putting a lot of intention into it not being a distraction (both within the app, and outside it).
> our notifications will be easily manageable
Yep. "App XXX would like to send you notifications" -> "Do not allow" :)