I don't know about Unitronic specifically, but most stage one tunes can improve mileage slightly. However, they often do not because it is often difficult to avoid using all of the extra power they provide. If you drive the car very conservatively, a tune can make the engine more efficient (hence better mileage). More power requires more fuel. Therefore, if you enjoy the extra power very often, a tune can actually mean less fuel mileage.
Like all mileage - the way you drive the car has a greater effect than any modification you can make. Better mileage is not usually the reason why a person gets a tune. It is probably possible to create a tune just for mileage, but not many people would pay extra for it. Unless you can consistently keep your right foot off of the accelerator pedal, the best mileage tune is probably free (the stock one).
2009 Jetta SportWagen TDI
Build date: 01/16/09; Buy date: 02/09/09
Coveted Three Pedal Version, Big hole in roof
Dieselgeek Shortshifter & Panzer Plate (my favorite & my smartest mods)