Well, the answer is “no.” I was only able to use a credit card to upgrade my fare at the gate. LUV vouchers cannot be used for this purpose.

On a related note, it is apparently much easier for the gate agent to upgrade a fare for a “day of” ticket than a ticket on a different day. In the past I have had no issue paying to upgrade at the gate for both legs of a same day return round trip. But today, while it was easy for the agent to upgrade the outbound leg, the fact that the return leg is tomorrow presented additional challenges and it took much longer to accomplish. In the future I will likely restrict my request to upgrading same day flights, and if the return is on a different day I will wait and ask the gate agent at that time.