I'm referring to the older models of both the PS2 and PS3, not the slim models.
You need an adapter for the controller but yes it will. I would not use a power cable but if it works it works I guess.
The USB adapter works for me. On some video games like Soul Calibur you are able to press the analog button previously the controller will initiate working, and it gets fussy some situations having to unplug it and placed it back in.
Controllers, yes, you just need a special adapter. Power cable, absolutely not, since the PS3 Fat uses a 3-prong power cable like what computers use and the PS2 uses a completely different kind with only 2.