This is certainly possible - pl post details of OS, database and EBS versions.
Both outbound and inbound processing of workflow will need to be enabled.
Pl see the MOS Docs referenced in PO approval from e-mail notifications
I viewed the document, but the document does not focus on the steps of approving through mail only. (The user who receives a mail should not login to EBS to approve.)
You can approve a notification from email by just clicking on Approve/Reject link in email without login to application.
For this you need to do below steps.
1. The recipient user has the valid email address set, for which the email notification has to be received.
2. The recipient user notification preference should be 'MAILHTML' i.e 'HTML Mail with attachments', you can set it from preferences section after login with the user
3. You can see the notification preference and email address details from wf_local_roles table..
4. The notification Mailer should be up and running (Outbound thread count should >=1 and Inbound thread count = 1)