Thanks for all the replies.

Here's what happened. Like Miikka the thought of sitting in a fully booked economy cabin freaked me out so I asked one of the ladies in the CPH lounge to put a note in my reservation that I was willing to use 30,000 points to upgrade.

I got to the gate about an hour before departure and got in line at the desk. When it was my turn a very nice woman told me that she had already upgraded me to Business class and printed out my new boarding pass. She also said that she had done it without deducting any points from my acccount since she had needed my economy seat for a family that wanted to sit together.

I was very grateful but also surprised that they hadn't just taken the points out of my account since I had clearly let them know that they could.