For the specific admin or manager users that want Visibility into orders (in the case of shared roles not wanting to order duplicates, etc), but do not require Approval, and do not want to delay orders.
Ideal solution would be to specify this in the Email Notification setup. However, the logic needed to achieve this goal seems to be present in the Approval Workflows. We would just need the ability in the "Allow Approver to" selection to "Review Only - No Approval Required".
The same email could be sent with the links to review but no approval needed.
Ideal process may be to include an option for the Reviewer to click "Review Completed" to mark it off of their list. But ultimately, it would not hold up the order in any way.
Could you not simply add those users to the New Order notification? If they don't need to approve the orders, but want to see what orders are being placed, this should be suitable.