As long as your watch has a heartrate sensor, the watch calculates the Calories burned during an activity, using the detected heartrate (HR) and comparing it to your resting HR (detected during the sleep and during the resting periods). It means it does not matter what sport you do - whether it is running, walking, biking, or jumping ver a cord - it is not the name of the discipline that controls the Calories, it is the heartrate. So yes, Garmin watches can monitor the energy consumption even for your cord jumping.
