You would think so, but according to Geoff Johns' logic in this book - no.
For some reason known only to him Geoff Johns sees the classic silver/Bronze-age Joker as a different man to the one Alan Moore used for 'The Killing Joke'... So Jason Todd kills the classic Joker, 'The Clown' version according to Geoff Johns' view, and 'The Comedian' version, the one Alan Moore explores is the real Joker....?
The summation of Moore's take on the character in The Killing Joke was that he was insane, Bruce Wayne reacted to personal tragedy in a way in which he channelled his feelings and his life into helping others and battling the tide of criminality as The Batman. The Joker on the other hand, whoever he was before he fell into that vat of chemicals, didn't have Bruce Wayne's strength of character so let himself be swept away by events in his life to reinvent himself as The Joker. He would never have to face up to the real world, or himself, or his failures, because 'The Joker' was the representation of the madness that IS the real world.
I expect Geoff Johns is choosing to take Alan Moore's story and make the Joker's origin therein to be 'real' as it conveniently ties him in with the very successful film with Joaquin Pheonix. Moore never intended that origin to be definitive, he made it clear that it was highly subjective and unreliable as the Joker himself had no stable memory of the past or of his own origins. But it was a version that the film used, and therefore for whatever shallow reasoning Geoff Johns chose to make an previously enigmatic and dangerously unknowable villain to be entirely knowable, and actually quite mundane when all is said an done - because all he was was a loser who couldn't hack it at life and became the Joker.
We know who he is.
Think that would be better off having Bruce as the Joker, with his daddy as the Batman!