If the bottom of the tub is higher than the highest point of the trap, it'll drain. I would recommend a clawfoot tub in this picture, or at least raising the tub a little.
It should drain, but I would not want to need to snake this piping out if a clog forms. Main cause of clogs are hair and the residue left from soap and shampoo. A wire screen (the temporary removable type) over the tub drain would help prevent lots of problems in the future.