No. Batman's goal in that scene is to capture those men so that the police could use them to bring down Boss Grissom. Even if he was prone to murdering rampages, in that instance it would have gone against his interests to kill them. Later he he knowingly blows up Ace with many people inside while he waited outside.
The thugs he beats up in the opening scene are actually the first sign that this Batman is a killer. They talk about another crook Batman fought and very strongly implied that Batman killed him since the one who denies that Batman exists says that he "got ripped and took a walk off a roof, no big loss" and the other one talks about he fell "five stories straight down" followed by arguments over the state of his corpse and whether he was drained of all blood or his blood was all over the pavement.