I had no clue that this term existed. Curious, I researched it. From what I found, the term was coined during the Reagan Administration. Reading through the defining article, it seems that Democratic Education could be a good thing (based upon the idea that students become far more responsible for their education). That said, I do see two overwhelming problems. First, many students may not take being in charge of their education seriously and try to weaken the academic philosophies. Second, as with many words, the term democracy means different things for different people.
As some see in Democratic governments, problems arise quickly. Therefore, I would suggest that the education community faces enough problems. Giving away too much of the power to those who are supposed to benefit from it would be detrimental.