Did a couple quick tests since I was looking for the same answer.
Without adding as an additional mailbox, you cannot add it as a favorite. Use add additional mailbox and you can add it to favorites, but if you then remove the additional mailbox, the favorite drops.
That being said, I was surprised to see all the answers of "you need full access to the mailbox." That's just not true.
If you only want to see the inbox, grant the user whatever level of access you feel comfortable with to the inbox folder. Then, on the top level (where it has the email address or mailbox name), right click and select Data File Properties (2010) or Properties (2007 and earlier). Select the permissions tab. Grant only Reviewer access to the "top" of the mailbox.
Now, if you add using "Additional Mailboxes to open", you will only see the folders under the mailbox you have been granted access to.