After a close look at the pic I must disagree. Although the raised adjustment flats make it look like there is enough for engagement, a magnified view shows that the main face of the cup is recessed below the face of the lock ring by 1-2 threads. That is not sufficient engagement, especially as the OP indicates there is still play in the BB. In any case it's irrelevant as there is little doubt that the BB needs to be overhauled ("I've ignored it for two years...the amount of play is now effecting the gears.")