I'm not sure how many users will actually stay away. But if even a small fraction of the mods for these big subs stay away Reddit's gonna have a problem.
Lemmy will pull some mods away, traditional forums will pull some away, and that could really hurt.
However, only time will tell if that ends up happening.
Most mod tools and bots rely on API access and are just as affected by this change as third-party Reddit clients.
After the outrage started, Reddit has stated that they will make exceptions for mod tools and accessibility apps, but it requires manual approval, and a number are likely to be declined in spite of it. Particularly when considering that a lot of moderators made use of mod tools which were contained within these third-party clients that are shutting down, and are likely not going to be spun off into separate tools.