It might work OK. It depends on a couple of factors, though.
First off is the fairly simple seeming one of decoding the signal to the brushed motor drive into a form that can be used by the brushless motor controllers. This seems easy, but it needs to be fast, as any delays add to one of the time constants inside the control loop. I believe some of the quadrotor builders have found that all ESCs are not equal in this respect and that quadrotors need ESCs with a fast response. In this case you also need to make sure that your decoding circuit will have an equally fast response.
The second potential issue depends on the loop constants being sufficiently tolerant that they will work OK with a bigger machine with a higher mass. I suspect you might be OK, as the problem is probably worse when going from a slower response machine to a faster response one, but there may be a degree of control overshoot because the system will be tuned to expect a faster responding quadrotor. The speed of response for these things is largely a function of size and mass, as it's primarily driven by the moments of inertia around each axis.
Sounds like and interesting experiment, though, as as some of the smaller brushed motor quads are fairly cheap, you won't lose too much if it doesn't work.