As long as they don't clear their cookies the PM's will stop. If there is no cookie one is set with the current user number. Even if you log out this cookie will remain. If they log back in under a new user the new number is added to the cookie and a PM is sent. Now that the cookie has two numbers stored it will take a 3rd new number for it to send another PM.
I'm not sure which would be better for an ignore feature. Something from the configure file in the admin area where user numbers could be stored or to create a whole new field in the user's table and set a flag value to ignore the users with the field set.