What would happen is you would have the Totals section of the order displaying the Discount Coupon Description right in the middle ...
Currently ...
In the Order, the Store Owner can click on the link for the Discount Coupon for a popup for the description ...
On the My Account the Customer can click on the link for the Discount Coupon to get a popup with the description ...
The Customer can go to the Information box and click on a link for the Discount Coupons and get a page with the description ...
In the email, just the Discount Coupon code is displayed in the Totals section of the Order email ...
Adding the Discount Coupon description in the middle of the Order Totals is going to make things very difficult to read ...
This is why I suggest adapting the email that is being sent out where you can add the code I posted somewhere in the email to give the summary in a clear and concise manner so as not to confuse the Customer or cause confusion on lost of information in the Admin Order for the Store Owner ...