Yes he would have, because he wanted to kill Superman, and like I said in the part of my post that you didn't quote, you can still set up a Batman V Superman fight without wasting time on a "Clark hates Batman't methods" subplot. Look how simple it is to set up Batman using a Batsignal to call Superman without the "Clark hates methods" subplot.
Lex invites both Clark and Bruce to the party because he already knew who they were. That's when Clark learns Batman's identity and that he's trying to get something important from Lex because Lex might not be a good guy, so Clark investigates the issue, Bruce does whatever he did in the film and when Bruce/Batman goes after the Kryptonite,
he runs into Superman who is after the same thing, Batman shoots Sups and tries to put up a fight because his motivation has already been established and Sups is just trying to explain that they are both after the same thing...and their encounter ends with Batman letting Superman know that "he will bleed" and telling him next time you see my light in the sky, come find me. Done...no scenes of Clark arguing with Perry over Batman's methods and him getting photos from Lex...and non of that nonsense that has ZERO effect on the actual fight, from Sups point of view. In the end, the batsignal is just used as a tool to call Superman...it's not really bait since Superman is not like, "How dare him turn on that light after I told him not to use it!" He already knew Batman wanted to fight him...even Lex told him