No, that setup will not provide any privacy. In order to enforce any isolation between user accounts, they must not be given administrator privileges.
Any user that is an administrator can easily read the files from any other user. They have access to the "sudo" command, that gives "root" privileges in the underlying Unix system. They have the ability to change the login password of other users. This would enable them to log in as the other user, and see their Safari bookmarks or saved tabs, or any other file or information, provided it is not protected by encryption based on a password separate from the login password, such as an encrypted disk image.
If iCloud is already enabled and the computer is a "trusted device" for things like Contacts, Calendars, etc., or iCloud Drive for other apps like Pages or non-Apple apps, then by logging in to the computer as that user, another user could access those iCloud files. Furthermore, they might have access to the user's e-mail if they use Apple Mail or some other e-mail app on the computer that stores the e-mail password. In that case they may be able to log in directly to icloud.com or appleid.apple.com by changing the iCloud/Apple ID password.
Some of this information could be accessed without the other user noticing. In other cases, the user would notice their passwords being changed. It is not possible to find out what a user's login password is, only to change it.