Um, no.
The point is that there are 3 issues propelling Batman's desire to kill Superman: inadequacy (this super powered being comes out of nowhere, makes him feel small; resolved by a) beating his ass and b) the Martha moment shocking him into seeing him as just a person with powers), legacy ("if this super-being comes along, what good am I," again addressed by the realization that he's just a person), and finally the semi-rational fear of Superman. This is mostly a rationalization constructed to justify his feelings resulting from the previous two motivations; once they're gone, this would be weakened considerably, but even if it wasn't, Superman turns around and dies for the planet, thus making it clear that there was nothing to fear from him at all.
Batman IS fundamentally changed by the events of the second half AS A WHOLE. You don't get the cut off the ending of the movie and turn it into a gotcha.
First off, the first two you are redundant. Feelings of Inadequency could easily be the result of feeling his legacy isn't recognized in his presence. I mean, either way, it boils down to Superman making his dick feel small, so it's the same general idea.
His inadequacy is resolved by a fight where Superman wasn't even trying to fight him? And how would recognition of Superman as a person make him feel alright about his legacy? Unless Batman is a complete moron, (which is he, I guess), these issues aren't resolved at all. Batman didn't 'beat' superman, Superman just didn't want to fight him, even as he fought back (which is another issue entirely, but whatever), and Batman realizing that he's a person doesn't mean Superman's presence won't outshine is accomplishments.
It'd be better to say that Batman's resolution to the legacy is to make the JL his legacy, by organizing the team of super powered beings, if anything, but I'm willing to bet anything that it's just a happy accident we could use that as an excuse
The only resolution that works even a little is his recognition of SUperman as a person, but the previous aspects haven't been resolved at all.