I discovered this the hard way. iOS backups using the iTunes application will overwrite any older backups. I made a backup of iOS 10.3.3 and then updated to iOS 11 beta, then immediately made another backup. Then I discovered that an old app did not save data in the usual way for iOS apps; it only allowed exporting as CSV. I previously made manual backups of all applicable app data in installed apps, but this particular app did not have one.
So, I have likely lost the data in that app. I happen to have a 10.3.3 backup from this morning in Time Machine. We shall see if it works.
UPDATE: Time Machine did capture the last 10.3.3 backup, so I can downgrade. Once again, a reminder that backups are a good thing.