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.
Yeah many people don't really realize just how bad it is when moderators leave, especially for a platform like Reddit where the mods are unpaid volunteers. On a different platform where they pay moderators they could just hire new ones, but with Reddit currently hemorrhaging money they are very much not going to be able to hire brand new moderators for every mainline sub.
Plus you have to account for the fact that while there are people who might be able to take their place now that number will quickly diminish I say become swamped with work and lack the proper tools to do decent moderation. It does not bode well for Reddit's future.