Hard to imagine that itty-bitty sensor being so much trouble! But if it is shorting, sure could draw down the battery. Easy to check with a multimeter though, or simply disconnect the connector with the engine off and check the amp draw on the battery before/after.
Good time to make sure the connectors on the sensor are clean (electrical parts cleaner/MAF cleaner, or simply compressed air), as they can also cause a short when put together. After cleaning, add some dielectric grease before snapping back together, helps keep water & dirt out.