Of course this will work; you are driving a generator using a motor. In engineering, this is called a motor-generator set. We often use that to have special equipment that run at 400Hz.

Are you thinking of a perpetual motion machine of the first kind? No, then it won't work.

Perhaps others will be able to explain you better. Better to consider the angular momentum vector: do you want them to cancel or add together? But over a complete precession cycle, the net angular momentum will be zero (in either case).