1. Yes, a gradient is required. If the energy of the diamagnetic material does not change, there cannot be a force, as this will violate conservation of energy. You are proposing a perpetual motion machine of the first kind.
2. The quantum nature of diamagnetism doesn't matter in the slightest to the argument being made, so why are you bringing this up?
Diamagnetism works by inducing dipoles in the medium, and a dipole placed in a constant field experiences no net force. It may experience a torque if it is not aligned with the field, but in the case of diamagnetism the induced dipoles are naturally aligned, and so there is neither force nor torque.
Potential energy changes when moving parallel to any field force, regardless of whether that field is static or has some gradient.