Implementing a quadtree into C2 wouldn't be that hard; especially as there is an API ready to be turned into a behaviour. The down side is that like C2 Physics which is Box2D, it's an entirely different collision check.
This means that like the Platform/Solid/Jumpthru/Bullet behaviours this Quadtree would not be compatible :( You couldn't take advantage of say Bullet Bounce off wall, and use Solid. Those are built to work together. Where as Bullet and Physics won't.
However, if you don't need Platform and Jumpthru. It can be created and implemented to good effect. The best solution is for Ashley to implement a quadtree into the natural behaviours. Might even be possible to slip it right into the basic object collision making the overhead minimal. Maybe next time there is a poll we should suggest it :)
But in the mean time maybe someone or myself if given the time can look into a behaviour.
So I tried the demo. One of the options is 500 objects. In a brute force model wich C2 uses. That would be 252,000 = 500 x 504 (+4 for walls). That's a lot of collision checks. Where as in this it looks like maybe 200-500 checks or something like that. Certainly not 200k+