Yes. Open the customer's profile (Users, then edit the customer) and click the Communications tab. It shows an Email History table - every email logged to that customer's exact email address, with ID, Date, Subject, Template, Protocol, Status and Opened columns, newest first.

Click an ID to open an Email Details window with the same fields as the main Email Log: Recipient, Subject, From, Template, Protocol, Date, Status, BCC (and Redirected To, if the email was diverted), plus an Open Tracking section with Opens count and First/Last Opened.

This tab only requires permission to view Users - you don't need the separate Email Log permission to see a single customer's history this way.