It's important to realize that an ordinary Archimedean screw gets water and air
alternately simply by the fact that the "snout" (the end of the hose) dips
into the water and then back into the air.
An Archimedean screw is simply a wedge wound around a shaft. It can be
enclosed in a tube or sit in a trough. For pumping water either will
work but the end is not moved in and out of the water. What ever air is
moved is incidental to the process, not a part of it.