This is known to be kind of true. At least some part of the body remembers the pain. And it can have some long lasting effects (chronic pain, or stress). That's why nowadays during many surgeries they try to suppress the pain as much as possible locally.

So if you get surgery on your leg, it is best if you have additional anaesthesia or pain killers working in this particular leg. So you wouldn't feel all the pain even without general anaesthesia.