You are assuming the BTC are still in the account of the person who "owned" the address. And the internal ID would just show that a deposit came into the said address and that the proper user account was credited with the BTC. None of that will have any of your information in it.
Correct, I am assuming that once the money is inside MtGox they log all the internal transaction with BTC addresses. I know they log them because I have account history. I assume they are associated with BTC txn data because I can't see it working otherwise.