I would bet that the ortholinear layout and simple button spacebar they put in that device kills any productivity gains you would have with a physical keyboard.
For a device of this size, I would measure productivity gains in terms of accuracy rather than speed. That is to say: I don't expect to type as fast as I would on a full size keyboard, but I would expect to be more productive than I would be with a touchscreen keyboard. Whether the ortholinear layout affects that, I don't know. Admittedly, the small spacebar buttons probably would.