Most of the time, they will still have internal records. Sometimes they only go by what is on your CR, so once they remove a late payment, for example, they will forget it was even there.
A friend of mine was able to GW some very old lates from a Citi account. Then he called and asked for a CLI and the CSR said, "I see you have an excellent history on this account." He almost replied, "Uh, if you say so," but bit his tongue.