The tc IS a pump, it doens't have a pump (that's what I meant).
It's not a positive displacement pump (like a PS pump), but similar to a SC roots air pump.
I'm using the vague term 'pump' to mean anything that moves fluid (as the stator and rotor fins to inside a tc).
I remember a very old automotive book my dad had that described a TC as two fans facing each other at about 2" apart. One fan is powered (by the engine), it spins, moves air (ATF in the case of a TC), and induces spin in the other fan.