It's an interesting idea. The number of 'throwaway' accounts on HN suggests there might be some value to a network where now and then a comment or thread couldn't be traced back to an account.
It doesn't mean at all that you would necessarily get more valid answers to your questions. If that were true, the boards on 4chan that aren't /b/ would be glittering beacons of civilized discourse. People given the mask of anonymity can act more truthfully but also deceptively because they don't bear the consequences of identity.
Of course, there's public anonymity and there's anonymity to the mods and anonymity in the database. If the NSA wants to know who's who in your network, encrypting messages and hashing IPs probably isn't going to keep them at bay. What will the server logs tell them, for instance? Or packet sniffing? Or planting a mole on your staff?
If you allow file and image uploads by anonymous posters, you WILL inevitably wake up one day and find a ton of child porn, that's just how anon rolls sometimes. How will you deal with gore, porn and copyrighted material? When someone makes a threat against another user and posts personal information about them, will you go to the police? Under what conditions would you as an administrator violate the anonymity of your users?
Maybe only allow the anonymous posters to post text, or make certain that the mods can tell which account it really is (although this by definition makes the system less secure for users.) Either way, I think you'll need to be prepared for trolling and mischief, have your moderators ready with a clear set of guidelines, and even a few rather fascist options available like blocking Tor if need be.