No. I'm an idiot. My drawing can't work. With a conventional hub, if the axle is supported on both sides, then the linkage between the rear wheel and pedals or idler has to go through the axle once every rotation.
To get around this you would need to change the way rear hubs work. The shaft needs to be at the end of the axle, hence outside the chainstay. Then you use a *rotating axle* along with bearings at the dropouts. Pretty weird.