The main problem with this approach is that there is no easy, convenient way to distinguish between cases closed by the user, closed by the customer, or closed by the workflow rule (at least, not without an extra field for flagging purposes).

If you're okay with a custom checkbox that will enable/disable the notifications, a trigger would be pretty straightforward:

trigger NotifyOnAutoClose on Case(Before Update, After Update) {
    if(trigger.isbefore) {
        for(case record:trigger.old) {
            if(record.auto_close__c) {
                trigger.newmap.get(record.id).auto_close__c=false;
            }
        }
        return;
    }
    casecomment[] comments = new casecomment[0];
    database.dmloptions option = new database.dmloptions();
    option.emailheader.triggerotheremail = true;
    for(case record:trigger.new) {
        if(record.auto_closed__c) {
            casecomment comment = new casecomment(parentid=record.id,commentbody='Case was closed because no reply was received from customer within seven days.',ispublished=true);
            comment.setoptions(option);
            comments.add(comment);
        }
    }
    insert comments;
}

Your time-delay workflow rule should set a field called auto_close__c to true (it should be a checkbox data type). The field update should cause this code to run.

The first section will uncheck the box if it was previously checked, in other words, if the box was checked when the transaction started; since the box has no other way to uncheck, we turn off the marker so it won't comment more than once.

The second section will create case comments for cases that were flagged as auto-closed. The triggerOtherEmail flag should cause self-service users to get a notification. You can remove the dmloptions part of the code if you plan on emailing the customer through the workflow instead of the trigger's case comments.

I think this should probably get you where you're trying to go.