Memories can be reference points for events with enduring impact, but conscious memory is a totally unreliable one, and the effects are what's important; evidence of them is only relevant as reminders. If you lost a limb its presence would be totally independent of whether you remember the cause, consciously or otherwise. A memory might help provide context and significance, but if you were unconscious at the time you'd experience all the same effects despite lacking any memory of the cause. That's an analogy and thus imperfect, of course (it's a lot more physically oriented than I think proper, for one thing) but it illustrates what I mean. More importantly, while losing a limb would radically alter your physical capabilities and perspective, it wouldn't alter YOU as a person, only your form and outlook. You wouldn't be able to drive a stick, but you wouldn't suddenly become a different person.