If choosing to disable the Notification Center toggle for an iOS app, does this mean that notifications can't be located after they've disappeared? When modifying notification settings for individual apps from within Settings app on an iOS device (by navigating to Settings app → Notifications → App Name), I've noticed that there's a toggle for the Notification Center.

If this isn't checked, does this mean that notifications for the app in question simply won't be delivered to the Notification Center at all, and impossible to locate if not initially interacted with?
What that switch does is reject the push from the server. One message might still get delivered if the server side doesn’t receive the message but the device send back a “we’re not subscribed anymore” message until you re-enable notifications.

Notifications can come from apps on the device or from the Apple Push Notification Service - so either way - those messages literally are stopped and discarded as opposed for them all to keep piling up and not being visible.