Checking in early increases your chance of getting an upgrade, but not by much. Having a higher status can help greatly.

CX may offer upgrades at check-in, in the lounge or at the gate, and most likely in the lounge of at the gate. They only offer op-ups at check-in if they are quite sure your upgrade will hold. Even then they may still reverse it at the gate (and it happened before, but very seldom).

If they offer you op-up at check-in, they already processed the op-up list and you are on there, but not because there is no seat left. They will upgrade a higher status passenger to leave a lower cabin seat for you.