In theory they should - only thing mod stores about them is energy when they are low on battery (to stop them) - it uses train ID and that changes (because trains do not teleport - they are destroyed and recreated). So if they move between surfaces when low on power, they lose even that charge. But i do not expect them to be able to move when low on power.
Everything else should be surface-proof.
I finished game before space elevators were introduced, so i have no experience with that. But because on surface is much lower solar power, i reccomend to power those trains throught internal modules (RTG or so) too.
