Yes. It isn’t actually a 404 when that setting is on though — checking the box changes it to a 403. I think that the <title> should conditionally reflect that, or it distorts analytics reports.
GA4 defaults to showing page titles in reports instead of paths/URLs, and the 403s are being listed as “Page Not Found”, which isn’t correct. It should be something like “Log In to View This Page”.
The reason I want that setting on is because the email digest contains links to private topics and if people click on those and they don’t see a message that they need to log in to view the page, they will probably bounce.