Norm,
That sounds like a lot of extra stuff to drag around with you. Unless you are into total fitness workouts I would think a guy might get awfully tired pretty quick and have to shut down too soon in the day, but it does sound like it would probably work. You could put cams on the axles so that when you pulled it the basket would shake enough to dump the sand. Of course it would have to be dry sand because the wet sand would clog up and wouldn't pass the screen, unless you had a spray nozzle. Then again if you are working the dry sand then there would be much more resistance trying to pull the unit through the dry fluffy sand. I guess you could always make a harness to drag it around with, but then you would have to turn around to dump your bucket, or drag the sifter up along side. Either way it sounds like a workout.
Believe it or not, there has been a magazine article and plans you could purchase to build a beach skimmer that you pull though the dry sand to find jewelry. I think it came from the 50's. I still see the plans in old books and magazines once in a while. Even before the days of the modern beach detector people realized the potential resource of items lost on the beach.
If you try doing this please keep us posted as to how it works out. Maybe you are on to something that you could put on the market. If you strap a battery to it and install electric motors and add a radio control unit I think you could make it happen. Highwater