Yes, components wake up and remain awake as long as the bike moves or vibrates. However, when you are not shifting, the battery trickle-down is incredibly slow. Additionally, sensors in each component ensure that they go into sleep mode automatically once you aren’t riding and vibrations stop. The system will awaken again once you pick up the bike again.
For extended transportation, SRAM recommends that you remove the derailleur batteries and replace them with the red battery blocks to keep the battery contacts clean. This will also remind you to install your batteries before you ride. Battery covers can be installed on the batteries themselves.