Honestly, I cannot even imagine putting a lock on our stroller. We are DVC members, so we go often with our 4 year old. The amount of time you would waste locking/unlocking the stroller would be way too much. My son is in and out of the stroller all day. And, yes, the CMs move the strollers all the time in order to keep them in an orderly fashion in the stroller parking areas.
We have a Bumbleride, which is a pretty expensive stroller, and have never had any issues with it being missing. I agree with the other poster, the vast majority of the time it is just a case of mistaken stroller identity. The one thing that I did do, was place labels in a few inconspicous spots on the stroller with our name, address and phone number. That way, the labels weren't easily removable if is was "stolen". Obviously, we don't leave our valuables in the stroller when it is parked.
Have a great trip!
Michelle