It very much depends on the route. Demand for J ex-US is ridiculously high right now (hence the stories about people with awards tix being booted out of J)
The OP seems to assume that cash upgrades are guaranteed; that is NOT the case. Calling to demand for something that you are not entitled to is unlikely to help. You can always upgrade if there are seats and meals available, but you have to pay to change your ticket and pay for the difference. It almost always ends up more expensive than having booked J in the first place.