I strongly disagree. Kat's commentary on Edwin, both when he's in and out of the room, run the attitude of "this boy is a marionette, and everyone can see his easily pulled strings but him." He doesn't realize how malleable he truly is be the likes of Ian and Chuck, and even with people he doesn't like, Edwin's strings can still be pulled by intentionally triggering his adversity (i.e. want Edwin to get angry, send him to Sampson). Chuck obviously wants to maintain the "there are no strings" illusion, and Edwin is so oblivious to it that his natural response is to lash out when somebody points out the strings, as he does with Kat and Abel. Of course he's right to then question if by pointing out some strings, the conspirators are themselves inevitably pulling on other strings, thus his search for Kat's and Abel's respective end-goals. Even Edwin is now starting to realize the pull strings, but he's not considering all the puppeteers, nor their full intentions. Now does Kat merely believe that Pinocchio's strings should be cut, while gaining what use she can out of an asset like Edwin, or does she believe that by empowering his sadism he will become even more controllable by her, I don't know yet.Tl;dr: ...and Edwin's too big of a variable to reliably plan around.
All that to say: Edwin is NOT an uncontrollable variable. Yes he may make a few individual choices that aren't in Kat's favor, but she's still herding him within the boundaries of her overall plan, whatever that may be. Whether aligning or resisting her, nothing Edwin has decided thus far can disrupt Kat's trajectory (except maybe fueling Hana's general anger and specific hatred of the Club, but that's too far ahead to predict final results).