Jim Garrison pointed me to this website for The Forum for Education and Democracy, which also has a blog. It's unclear exactly what they are doing, although there is this project page and they did publish this report on Guiding Principles for NCLB. The participant list is pretty impressive. Overall it seems like just another shell organization. To the extent to which it is as "empty" as it seems (the website looks like this even though the Forum was founded over a year ago), it may embody how education usually deals with "education and democracy".
Note also how their statement on NCLB lists relating schools and communities together as one of their three top goals, but how it appears in only one out of the six actual recommendations. Community engagement sounds good, but usually gets only pretty vague lip service. There seems to be a broader policy document related to the short recommendation piece, so maybe there's more there.
Maybe someone else knows more.