How fast can pushback tugs actually go? (maximum possible speed)
This AC covers a lot of the regulations around towing aircraft and according to the regulations 


  Towing Speed. Towing speed should not exceed that of walking team
  members. Towing speed should not exceed the safe operating speed for
  the conditions or the published speeds established by the TLTV
  operators published procedures.


In other words you can do either as fast as your operator says you can or as fast as the tug manufacturer says you "safely" can. The AC goes on to discuss a lot of other things but also mentions this tug in their section on tow-bar-less tugs. According to their website: 


  Unique hydrostatic drive for moving aircraft on the ground at up to 32
  km/h [~20 MPH] – without compromising safety


This is about the same speed that Terry discusses is the maximum taxi speed in this answer so you don't really gain any speed. Depending on the aircraft and airport in question you don't want to cut down taxi time to much as that may be an important time during which the engines come up to temp.