Sort of, Joker's backstory is kind of all over the place, half because different artists wanted to tell different stories, and half because Joker himself doesn't quite remember it clearly. The general gist is that he was a failed stand-up, and he wanted to rob some sort of factory where chemicals were used, so he became the Red Hood with a group of guys, ultimately Batman shows up and somewhere in the struggle/getaway, Joker is bathed in the chemicals, which bleaches his skin and gives him the green hair (and sometimes the red lips too). But like I said, it's very open, and Joker himself has said he likes his past to be "multiple choice" lol
In the classic origin story, Joker got bleached permanently by jumping into a vat of chemicals, trying to escape Batman as the Red Hood. The Killing Joke despite its flaws was a good take on the story. (Skip the first half if you get the animated version).
But yes, I like this take that the chemicals didn't actually do anything, and he was looking for justification to give his internal id expression.
