I used to regularly upgrade for cash on the ORD-CPH flight. It wasn't possible the other way. Upgrade for cash or for points has never changed the booking class, and as ksu states - it's only the booking class that determines the points. The only way to change the booking class is to change the ticket, paying the penalty charges (depending on the booking class conditions) and actual difference of ticket prices. It can be done, but would never be a good deal.