Can an alcove tub be installed with most of it behind a wall?
Alcove tubs are designed with flanges, or lips, on the 2 short ends plus one of the long ends.  The purpose of these flanges is to create an edge that the tile and backer board should cover, ensuring that water drips on the wall land on the tub.

Your design won't suit an alcove tub.  

However, you can install a 'stand-alone' tub and use a tile gasket seal around the edges that are to be water tight.  The gasket is a clay like substance.  You put the gasket in place and mold it to fit, then drop the backerboard on top of it to create a water tight seal between wall and tub.  Once the backerboard is water proofed you are good to go.

That said - the layout will be very awkward for getting into and out of the tub with this design.  I'd encourage you to reconsider.