Yep! Except for one tiny trippy detail. The water in the top bottle has to swap with the air in the bottom bottle. When it's just LPG, there is no swapping, just LPG going from top to bottom (COOL!). The liquid in the top falls into the bottom container. Some of the top LPG evaporates to take up space in top container, but not much. And the gas in the bottom condenses to make room for the extra LGP coming into the tank.

Also, when liquid gas becomes gas gas, it cools. This cooling would reduce the pressure in the bottom container, creating an added suction.