Not really. Hookwolf was a killer. Lung wasn't really much better on the murder front.Murdering two Protectorate heroes and a Ward, though, would. Otherwise, the whole "no killing (Protectorate heroes/PRT or villains)" unwritten rule would be a bad joke. In canon, the only ones we see clearly giving no fucks about that rule were the ABB--and, well, everyone promptly teamed up to take them down very quickly.
Kill Orders are not there to protect heroic capes from making a dumb move that leaves them dead against a villain out of their league. It's not even strictly speaking a mandatory Birdcage offense, though it would be fairly easy to get the jury to send a hero killer to the Birdcage.
What protects Protectorate capes from being aggressively killed is the promise of disproportionate retribution.
Simply put, if doing this didn't get him a kill order, then the "no killing" rule becomes an obvious joke and villains have no reason to hold back from lethal force against heroes (even Wards).
A Kill Order is a court order. The requirement is that the subject poses a clear and present threat to anyone, anywhere, and as such, a lethal takedown is functionally self defense, because they're going to kill you anyway if they are in your vicinity. This guy isn't nearly aggressive enough for that. Standard cop killer rather than Jack Slash tier.