Yes, unopened and opened PMs are stored in the member's inbox, until they are deleted. When a new message arrives, generally the member is alerted of its existence through an email to their registered email address.
I occasionally do get notifications of bounced messages to members' email addresses, but I do not recall seeing that NIIBE's email was included in any bounce notices. I will check them more carefully in the near future to see if any of the notices that I get pertain to his email address. I typically just delete bounced email notices that come into the 500Eboard.com admin email box.(admin@500eboard.com NOT PM)