The issues you are considering (distance between the carts and their possible gravitational interaction) are irrelevant. Internal conservative forces cannot change the total mechanical energy of the system, they can only cause conversions between kinetic and potential energy. The gravitational interaction between the carts is probably negligible, but that doesn't necessarily matter here.
Since the system is just the two carts, the gravitational force of the Earth on the system is an external force. i.e. we do not consider it in our potential energy. This means that we have an external force doing work on the system. I will leave it to you to conclude what this means for energy conservation of the system.