Most impractical in the form proposed, one must respect the enthusiasm (question the sanity?) the inventors in those days.
Its fun to try and reengineer it though! For instance, prehaps taking it in the direction of making the hull a rigid airship. Heavier than air travel would have been fairly impossible for that day and age, but a rigid zeppelin style craft might have been doable. I’m sure the arcamedes screws would not be great at moving air but I’m not sure they’d be any worse choice than much of the other proposed aeronautical propulsion of the era, and of you made that hull contain just enough gas bags to achieve neutral buoyancy it might have managed a hop flight?
It would make a great piece of art for a steampunk setting as either and airship or maybe a spaceship cavorite sphere style! The Merrimac of the Moon?
It’s truly a southern invention, those big screws would be bird strike city, so you’d get lot of fried chicken out of it. I think they may have accidentally invented the powered hand mixer here, so I suppose you could get a decent cooking use out of the working model as well.