The company 3D Robotics has a Drone (IRIS+) based on the Edison. Their prototype was based on the Arduino Expansion board. It could be of your interest.
You can also find a project using Edison as companion computer for a Drone in Edison for Drones | Developer.
The document Intel Academic Drone might be of your interest.
I too share your opinion. I do not see why the Edison wouldn't be able to fully control a drone. As you mentioned the Edison has RF (such as Bluetooth and Wi-Fi) capabilities that makes it convenient to control a drone. If you decide to continue your project and build a drone based on Edison, it would be very interesting and I encourage you to share it on the community.