Discussion boards can do this whether you are in a distance learning situation or a situation in which discussion boards are being used to supplement face to face instruction. Discussion boards build this feeling of connection by allowing for greater interaction.
This is particularly true in distance learning classes. One often feels a complete lack of connection to other people in the class or to the instructor. You never see them, you never hear them, and you never really interact with them. If you have a discussion board, that situation can be avoided as you at least get to do a lot of interaction in written form.
Discussion boards can even help in face to face classes. There is often not enough time in class to get into deep discussions. It is also common for various students to do poorly in in-class discussions out of shyness or some other factor. Discussion boards allow for more interaction and allow shy students to have their voices heard.
In both distance and face to face learning, discussion boards can help create more of a feeling of connectedness and community within a class.