Thank you for the explanationspoilers:end of spoilers
According to the internal logic of the series, no. In #2, the Comedian has memories of killing Jason and the Criminal is also implied to have the Red Hood origin. In #3, Batman discovered the Joker's identity a week after meeting him and it was the Killing Joke version. Joker's spiel at the end of this issue makes it clear (to me anyways) that the Comedian was always the true Joker. He was the Golden Age Joker who first fought Batman and he was the one who killed Jason. At some point prior to this story, he successfully created two new Jokers and, based on their appearances and professions, molded them into the Criminal and Clown, feeding them stories of his past exploits so they could sell the part, all as part of this grand scheme to f*ck with Batman by giving him a pointless mystery that ends with Joker supplanting Joe Chill in Batman's psyche. They were merely meant to pay homage to aspects of Joker's personality. The two of them never actually encountered Batman as the Joker prior to this.
At least, that's my take on it. But yeah, you gotta wonder why the Mobius Chair would've even told Batman this if two of them were fake, and why Batman was so perplexed by it when according to the internal logic of Darkseid War he could've simply asked the chair for more information. (And indeed, if he knew Joker's identity a week after meeting him, kinda strange that he asked the chair in the first place.) Then there's the Rebirth special's assertion that two of the Jokers had been arrested separately at Baltimore and Central City, with Batman still having no clue to the mystery.
Anyway, I'm just glad this charade is over with. Time to put Geoff Johns' career out to pasture, methinks.