Is there a way that I can add a discussion board to a blogspot site?
Probably not, in the same sense as you'd look at any other forum-board.
But, what you could do, is have your threads as posts, and let replies and such be comments to it. Basically, if all the different users (sadly, I can't remember if you can have multiple users at a Blogspot site, but I'm assuming it's possible) can also do threads (that is, posts), you basically have a discussion board.
Hope that helps.