Questioning short answer: are you sure? In the past, I've managed to get on to sold out flights operated by UA thanks to my SEN card. How it worked: the UA flight was a connection flight from a LH flight across the Atlantic, and the UA flight was booked under the LH number. So in that LH "contingency", I got a seat.
I recommend you simply call the SEN service, ask them to try booking you and see what happens.
Good luck!
Charles