facebook chat question!!?

on facebook chat, when you send a message when they still appear online in your buddy list, and then it comes up RIGHT when you send it that "message was not sent. user is offline." do they still receive it then?

because ive signed on facebook a few times before where messages pop up and i never saw them when i was online, so im assuming it was EXACTLY when i signed off?
 
No it says "user is offline so this message has not been sent" so i dont think they get it. However if you log out really quick and were chatting with someone and they sent you something and you logged right back in what they sent you would be there bc it was only a period of a few minutes. If that makes any sense.
 
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