No, but one of the characters, who is a transgender man, in episode 39, wears a ribbon that "turns him into a girl". In one part of said episode, he can't enter an organization because "he's a girl" and disguises himself "as a man" with a faux moustache in order to join it.
The first episode has Gino shoot himself in the face, but he almost immediately gets back up. There's also an episode where Gilmore devises a plan to steal Jesus's shoes which involves him, Gino and Khonjin killing themselves to get into Heaven, however the plan is never actually executed, until the bonus season.
There's a transgender woman who gets constantly misgendered and deadnamed by everyone in the show. This doesn't seem to affect her, however. It is implied at the end of episode 50 of the original run that she has amnesia and, therefore, doesn't remember that she's a girl.
Also, a gay character in one episode explains that he has a girlfriend. It was later confirmed that he was in a relationship with the same man from last paragraph.
Gay Spaghetti Chef and Khonjin are both gay and Khonjin is trans, and they die in several episodes, but because continuity is meaningless, they always come back.
A lot of episodes contain sexual innuendos or depictions. There is an uncensored gay sex scene in an earlier episode, which is later edited to have been censored (though only partially, and it is animated very crudely regardless)
In episode 26: Crimis, Santa's sleigh crashes into Khonjin's car. In Khonjin Takes A Break Episode 8: Shoes, Gilmore hits Gino with his car in a murder-suicide. In episode 54: Heist 3, Khonjin and Gino crash their car into a rectangle during a police chase, the scene is shown again in a "previously on" section at the beginning of episode 55: Heist 3 Part 2. In episode 80: Finale, footage of a car crash is played after the locksmith shoots Khonjin.
One example is in the bonus season when Gilmore hits Gino with his car in a murder suicide. This was because Gino refused to aid in Gilmore's "Kill ourselves, go to heaven and steal Jesus's shoes" plan, so Gilmore killed him, essentially forcing him to help the plan.