I did a test using a second logon name that I created just for trying out things like this. Unfortunately, once someone's mailbox is full and you try to send them a message, even if you have "Save Copy" checked, it does not save a copy unless it can deliever the message.
So, if you see the "PM box full" message when you try to send something, the message that you tried to send did not go to their box, it didn't go into your "Sent Item" and it doesn't show up on your "Message Tracking" list. Just for reference, I think you will find that the "Message Tracking" list is just that, a list and not actually a copy of the message that you could view.
This might be something that I will suggest to the vBulletin folks to save a copy of undelieverable messages no matter the state of the "Save copy" check box. Right now, it doesn't matter whether it is check or not, the message is not saved.