Would it make sense to use screw- and fin-like bending surfaces for propulsion (like what eels or the king of herrings have but in the atmosphere) instead of regular propellers or even flapping wings if you had super-strong materials that could change shape very fast? And if those materials had high energy conversion efficiency, but energy demands were still a concern? If not, how much thicker would the atmosphere have to be for it to become preferable? We are talking about heavier than air, high-speed flying machines.
The principle of screws as propulsion works as good as it does in water, because water is non compressable, meaning the screw can't not press the medium outwards. With air however you loose way to much energy to air that gets forced to the side.
You could of cause make a screw with a very small core relative to the diameter, but then you could also use a normal airscrew and reduce the drag.