I was flying FRA-PDX last fall and had 2 printed SWU with me. My wife was on award ticket and I was in H. I asked to upgrade us and they only had one seat -- which they did from my paid ticket (and I gave it to my wife) -- but they never said "no" due to her award ticket.

Last month I was flying PDX-FRA on an award ticket in Y with my wife and son. I wondered, like you, if it would be worth carrying the SWU just in case. I didn't have them printed but then we were op-upped to C due to an aircraft substitution!