In normal flight the thrust levers are set to what is called the climb detent which represents climb thrust. The autothrust system then automatically controls the thrust in a range from idle to climb thrust depending on the circumstances, and no, the actual levers do not move.
If the autothrust is inadvertently disengaged either through a fault or by pushing the AT button on the control panel the system interprets that as an "uncommanded" disconnect and freezes the thrust where it was when the disconnect occurred. A repetitive tone and caution message is displayed until the pilot moves the thrust levers manually, and then the thrust acts conventionally according to where the thrust levers are placed.
If the pilot disconnects the autothrust through the push buttons on the thrust levers the engine thrust goes to where the thrust levers are set, in this case climb thrust, and the thrust is then conventional according to lever placement.