I think you're right if there's an open tube, but with the mesh, the viscosity of the fluid, and the vacuum's resistance to flow might be enough to slow it down. If the mesh is properly fitted to the sides of the juice feed tube, the liquid has a high enough viscosity to resist flowing, and the tank is sealed properly to maintain a vacuum, I can see how it would work.
But, then again, I can also envision it pushing through after a number of hours when inactive and the juice feed is not burned off. When you consider period of inactivity, couldn't it be stowed upside down with the juice away from mesh so a few draws (inverted) would essentially 'empty' the wick?