My initial intuition to your last question was, “No, suffering usually entails some sort of looking-back process that places the pain in that context.”
I then realized that animals can suffer, and either I’m confounding Buddhist and Western psychological definitions of suffering, or suffering doesn’t require consciousness of it occurring for it to be suffering.
I hope that makes sense!
The difference is that when an animal suffers, they retain memories. One only need to consider something like this story I heard about a dog on Reddit, who was scared of obese people and men. Turns out, the dog was severely abused by a 500-lb man who was its former owner.
Instead of interviewing patients supposed to be under drug-induced amnesia, and finding the few who remembered, ask the doctors and nurses who are being asked to restrain patients in distress. A specialist in a procedure that requires light general anesthesia would, if this was true, have done surgery on thousands of people in various degrees of distress.
To me, that would be a pretty heavy secret to carry, and a 'conspiracy' that large would be impossible to conceal. I do agree, though, that pain without memory is pretty much as good as no pain. When you're conscious but unable to remember being conscious, are you still capable of suffering?