Just what I have seen happening:
- Staff in my origin isn't able to check me in - they call to SAS operations and clear my new seat in Y/C
- Staff in my origin isn't able to check me in - nothing can be done, try again in the next station (ARN or CPH) - gate usually has new boarding pass already waiting
- In the origin I ask to buy an upgrade for Y or C - they put a note in my PNR and there is a new boarding pass already waiting when I get to the next gate, they ALWAYS seem to prefer to take someone's points rather than upgrade some Gold (actually very good business behavior)

I don't ask for upgrade, I do not have such speech skills. If I do not get an op-up I just punish myself in Economy or then use points. Last February did something totally stupid (shows my passion for SK C), in SEA I asked for an upgrade with points, after couple of hours they informed me that I have been upgraded to Extra as an op-up but I could still get into C if I want ... with full points. I took the C and lost the 30k points. Oh man, I am hooked for the espresso machine and C meal service (and way better service in C).

So, my advice. If you really want your upgrade, then you need to guarantee it with points. If you do not want to lose your points, then it is adviced in many threads that CPH staff at the gate are a little bit odd - they do not always look for Golds and upgrade randomly. I haven't seen that in action because I usually take ARN route. ARN is always very good with upgrades but it seems that Extra is not selling very good and there is usually enough upgrade space in Extra and you do not get into C. Or then I am just unlucky nowadays.