As I understand it (someone more knowledgable can correct me if I'm wrong) DFA just basically means "put this guy in limbo to free up a spot until I figure out what to do with him." So you can waive and DFA. The DFA gets him off the 40-man roster, but he still has to clear waivers to be demoted.
And why are you demoting Bogaerts anyway, trade him to me.