I think it could work even with the mind rape and all. Kaworu is good at reading people, he easily figured out Shinji's hedgehog's dilemma and knew he was a delicate person deep inside. He probably would be able to tell that Asuka's bravado is only a facade he's putting up to protect himself and that the real him is more complicated and fragile.
Their only problem would be "time". It'd take a lot of time for Asuka to genuinely open up to anyone, and if their encounter is as short-lived as Kaworu and Shinji's then the scenario where Asuka saves Kaworu is doomed.