If they do take it to their own pile .. isn't this kind of mixing coins since all on going trades will be in one big pot?
Just now I traced few of my transactions into localbitcoin and also withdrawal from local bitcoin,you are right all of them going into huge pot which might not be possible to trace your funds but localbitcoin does know all these things and they can report the details to government if there is any complaint against you for laundering or other reasons,and also they will block your account with all of your remaining funds for violating their terms.