Is it possible to use Ethernet connection on Mac without battery draining?
It might be possible that some software is using up battery power. It can be checked in Activity Monitor under the Energy tab.
Under same app usage, ethernet adapter consumes more power.

The Ethernet dongle can be using up to 2.5 watts, that's 2500mW.....native ethernet connections typically use a lot less, but the dongle to ethernet requires MORE power, ..hence more power out when using the AIR thru the ethernet dongle.
Wi-Fi in GENERAL consumes between 10 mW and 800 mW (transmitting full bandwidth); NATIVE Wired ethernet consumes 200mW to 1W

Source: https://discussions.apple.com/thread/5194898