It’s really a good question. From the story standpoint, obviously they would’ve come up with something or there would be no- how. But from a “if Castle and Beckett real people” standpoint?
I think Castle would have eventually come up with something, because if you look at that episode, if you look at how are left and he is to tell her. He doesn’t want to screw this up, and at that point it’s not just for his little fun and games either. I think he genuinely wants to help her, and he finds himself stuck as far as what that means. He’s actually pretty broken in the last episode of season one at the thought of what this is going to do to her into them I’m not sure he would’ve given up quite so easily.
Kate, too was really disappointed when he left, he could see it all over face, while she struggled for a minute, it didn’t seem like a terrible hardship to allow him back once he apologized. So I think it’s some point, even if he hadn’t had the assist from Alexis that he did in the episode he would’ve figured out what needed to be done.
Basically if it didn’t happen then it would’ve happened eventually, or something would’ve put them back in each other’s orbit. Because these were two people that even then you got the sensation, weren’t necessarily as willing to give up on each other as they appeared.
I also like to point out that this happens to Castle as well, in Season 4 when he finds out that Beckett knew all along.
In my opinion, aside from the Beckett waiting for him to say that he loves her again just for confirmation thing, when Castle inadvertently heard her confession, deep down he wanted her to apologise hence his actions and it’s not just because Beckett wasn’t ready or she is but it’s not him she wants. He did repeat what he said when she was shot in their confrontation and she did apologise when she went to the loft. Would Caskett happen if both didn’t do what they wanted from each other? Yes. Some other event will make it happen, say in 505.
As for the S2 one, my alternate story is Castle would probably still be in the precinct as consultant, although possibly not with her, since he was still “researching” for his book/s. Then the events of 213 happens. That’s when she finally accepts that Castle is someone she can trust, someone who will be there when something happens, someone who has her back (even if this was voiced out in some Season 3 episodes). So, yes Caskett would still eventually happen.
PS I just realised that somehow this happened in WITCH, if anyone knew that Italian comic/magazine about 5 girls who have elemental powers. They were shown the What If they didn’t accept their powers at the moment it was given to them. It would still eventually happen, much later, when they were ready. :p