Not based on the Minecraft engine. The Minecraft engine is proprietary and closed-source. Also, it is (according to the developers) a bit of a runny mess, so licensing doesn't make sense either.
Leveraging "a bit of a runny mess" doesn't sound like it would make progress quicker. And, once the voxel rendering is implemented, is there that much more for this game to borrow from Minecraft?
I hope they borrow ambient occlusion. It makes it possible to see the edge of a voxel that's in front of an identically colored voxel, and makes the whole game much easier on the eyes.