Will a message be sent even if the Sentbox is 100% full?

Yes. When the receiver opens their Inbox, a copy of the message is put into your Sentbox. If your Sentbox is full, no copy is made.

The board's personal messages are meant for establishing offline contact with other board members. If you need to frequently correspond with another board member, use the e-mail button so they can respond to you directly via their e-mail client (Outlook Express, Thunderbird, gmail, etc), if they wish. In other words, the board's e-mail button allows someone to contact you without the need to know your e-mail address; the return address is set to their e-mail registered with the board.