Technically, no. Practically, yes.
The 4-port passive hub simply takes the RS485 data pair from the input connector and connects it in parallel to the 4 output connectors. It then takes the 12V power from the green connector and connects that to the 4 output connectors.
Technically, using this on DMX could cause reflections on the signal that may cause erattic operation and flicker. In reality, however, for the length of runs we usually use, it will likely work fine. I would try to keep the output cables short and of similar length, but that probably wouldn't matter much.
As for the general idea of injecting power over the same cable that has DMX, that's fine; it is commonly done for color scrollers, gobo rotators, irises, and the like in the theatrical world.
A true DMX spitter, like Chris says, regenerates each output independantly.
/mike