Just to clarify - the TU-2 is not a power supply. All it does is take the incoming power and bump it back out through the "power out" jack. The adapter is doing all the powering, and hooking up a regular daisy chain cable (the type that starts with a female plug to accept the male adapter plug directly) works the same way as running the power through the TU-2.
It can, however, serve as a neat connection point for the adapter cable - instead of hooking up to a plug on the end of a wire, you plug it into a pedal. But technically that's about the only difference.
Does anyone know if its possible to hook the TU-2 to one of the outputs from say a "Big John" and then distribute the power from that? Or would it overload the "Big John" (it can handle a load of 600mA for all 7 outtakes)?