Online check-in doesn't reduce the chances of an op-up: if the flight is so oversold they are looking at op-ups before 24 hours, they will already have a manifest with people and their Skywards status and selected status pax for upgrade. If they still need to offload after all cabins are full, they will look for volunteers at check in first. If it's not that oversold but it gets to that stage on the day, they once again have the lists of status pax and look for volunteers first at check-in. It's quite rare to have involuntaries for anyone who has status, or indeed is even a Skywards member. Also extremely rare for one person on a PNR with multiple pax to be offloaded.

Regarding compensation: if involuntary you will of course by offered the 600 EUR etc. However, voluntary offload compensation on EK is usually a return flight free of charge on the network (with booking restrictions). If they still need volunteers on the day they will be roaming for no status solo travellers at check-in at first, and if not then it's up to the controller.