Messages you send to someone you're not connected to on facebook arrive in their other folder
the question is, if you send the message and afterwards they accept the friendship request, do those messages move to their regular inbox so they can see them? or they remain on the other inbox folder?
It depends on their privacy settings. I think mostly, if you're not 'friends', the message will go into the 'Other' folder. I think if you keep messaging them, it will move into your normal inbox eventually