As long as tension was on the cord, Shawn, the device could lean to one side (the weights would perhaps have an average CG somewhat displaced when they spun than when they were still.)
The device cannot invent momentum, it must gather it from somewhere and move it somewhere else. Machines like this have been designed since the beginning of time. Mr. Newton would not be amused that 500 years after he explained why things work, there is still a cult that can impress some folks with sketches and such.