I agree, the chances of getting upgraded to a suite are miniscule. You might be able to get into a suite at checkin for less than they are quoting at CRO, but for free, it's almost unheard of.
I think the only times I've heard of someone getting upgraded to a suite for free was when there was an issue with their reservation.
We once paid to upgrade to a 1BR suite, and they upgraded us to a 2BR suite for free. Now, that said, the second BR was a lock-off and was not usable for anything but being a second bedrom for that room. So they couldn't rent it, and cleaning it was the only loss they incurred with the upgrade. This was at the AKL, where we were repeat guests and celerating a birthday, which I think helped. But again, we paid for the upgrade to the 1BR suite, so the comp was the second BR.
You'll likely be able to get a comp upgrade to a better view, or perhaps a deluxe room if you ask nicely and there is availability. but I wouldn't hold my breath for any upgrades past that.
Good luck and have a great trip!
Anne