Well, that shouldn't be an issue this time around, which ought to at least be a mitigating factor. Kaworu's still going to have to talk fast if he wants to convince Shinji that he doesn't want to be humanity's enemy, and I still think he's going to have a better shot at it the sooner he tries (which, considering "Cards on the Table" is neither this chapter nor the next, has me less than optimistic...), but unless something happens to Asuka and Rei (and maybe Misato), Shinji's not going to be in a position where if he doesn't have Kaworu, he doesn't have anyone.Shinji... reacts badly to the news that Kaworu has been lying to him, and "betrayed my feelings, just like my father!" Shinji, desperate for someone to be kind to him at that point, had opened his heart to Kaworu... and did not take the betrayal well.
Whether Kaworu has the capacity to realize this is another question. On one hand, he's apparently seen canon play out enough times to have a good idea of what happens and to know that he doesn't like it. On the other hand, he still doesn't seem to quite get humans, so he may not be able to figure out why canon happens or how to change it for the better.