Yes, but it would be highly unrealistic. The reason humor exists is it's a coping mechanism... people make jokes to deal with uncomfortable topics or get through fears. It's not that it detracts from the work... it's that in a real situation, someone is going to try and bring a smile to the room, even if they're in an inappropriate situation. The work need not be comedic to have a moment that induces a chuckle in the audience. Consider the original film "Terminator" in which the emotionless robot is sent back in time to kill the woman whose son will lead the fight against the machines in a post nuclear war. It's a grim premise... a lone woman is being hunted by a vicious killer with no remorse to kill her child, who has yet to be conceived at this point, and even if she wins this fight, there's still that nuclear war and machine take over in the near future of the film's timeline... and yet the most memorable line in the film is from a joke:
Terminator: I'll be back.
It's not even the punchline of the joke, but the set up. The Terminator gives the line to a desk sergeant who will not allow him to speak to Sarah (the woman he's trying to kill) because she's being questioned at the moment. The Terminator gives the line and quietly leaves... and then immediately drives a stolen cop car into the office lobby and proceeds to a violent attack of anyone in the station. The gag of course was the delay between the line and the return left the audience aware something is going to happen... the terminator's lack of subtlety and directness of his word choice were well known by this point in the story. They were anticipating the promised return to be a lot less quiet and polite as the scene had been... but his choice, and the almost immediateness of it was so over the top it became the film's most memorable sequence. It should also be pointed out this "joke" wasn't a joke in universe... the Terminator was deadly serious and wasn't setting up a joke, but a threat... but the dramatic irony of the dialog vs. the action was entirely written to make the audience laugh (though director James Cameron thought it would only get a laugh on a second viewing, and was floored that the audience got the gag on a first watch... he thought they wouldn't understand the Terminator's Character that quickly but was proven wrong.).
In real life, people who have to deal with a lot of gruesome situations like emergency responders and doctors/nurses often develop dark senses of humor. For example, the unofficial motto of many police agency's homicide division is "Our day starts when your day ends" and is only unofficial because the public would not appreciate the motto. Other cops are known to show up to a very bad accident and declare the victim DRT (Dead Right There, playing off the usual "Dead On Arrival" declaration done by EMS)... and if it's a really bad scene, they might declare the victim DRTTT (Dead Right There... and there... and there...).
It might be that your jokes aren't working not because jokes shouldn't work in a dark setting, but your own humor style isn't what the reader expected. As you said, it's an abridged universe style, which relies on meta humor and understanding of the original work being parodied to work... that is, the humor works because the characters are pointing out the absurdity of the work. While there is a place for this, if you are writing a series, it doesn't mean jokes and gags can't work... just that they must be self contained in the universe or something that happens to everyone. Consider the start of a minor chase scene in Disney's Zootopia... the heroes are spying on the villains when their cover is blown... how? By one of the heroes forgetting to turn her cellphone off... but the funny part comes when she looks at the caller ID and sees it's none other than her parents... everyone has had a moment where their parents call at the absolute worst possible time... few have had it where you're trying to spy on someone who might kill you if discovered... but hey, it happens to the best of us that parents call when it's not a good time...
The reason humor is necessary, nay, nearly required in especially dark and grim works is that it allows the audience to "breathe" a little. If you look at just about any television show and look for the funniest episodes, chances are they occurred right after a big dramatic episode. A great example of this would be the release order of films in the Marvel Cinematic Universe... The Avengers films are usually the capstone of their "phase's" dramatic tension... where all the events of the movies prior to that come to a head... but with exception of the original Avengers, they don't end the phase... but rather a goofier entry does. For the second film, it was followed up in the same year with the release of "Ant-man" which milked a lot of its humor from the very nature of the idea of a shrinking superhero... there's a lot of big explosive effect shots... only to see a pull back to the actual normal human scale of the fight to show the small puff of smoke that is barely noticed... Avengers: Infinity War was immediately followed up with Ant-Man's sequel, which continues with similar gags and Captain Marvel, which pokes fun at early 90s trends and cultures. And Avengers: Endgame is followed up by Spider-Man, far from home, which has several gags that explore the oddness of the events of Infinity War and Endgame (such as half the population of the world disappearing for 5 years... and suddenly reappearing in the exact same spot they were when they disappeared... and having not aged a day (One student goes on at length about how he disappeared but his younger brother didn't... and when coming back his younger brother is now the "older brother"... another character tries to use the technicality that he disappeared when he was 16 and should be considered 21... and thus can drink alcohol... It also did cheesy "in memorial" film in the opening to people who died in Avengers... Even the first Avengers film had a light hearted follow up with the Iron Man III, which was clearly shot with every 80s action movie premise in mind and unapologetically enjoying itself on this front. Other dark entries like Captain America sequels were followed by the zanier Guardians of the Galaxy films (any film where a talking Raccoon is a superhero is going to be comedic on the outset).
The reason for this is simple: It helps the audience cope and deal with the very serious nature of the premise of the work and identify with the characters. Prolonged stories with nothing but dark premises and characters who are not enjoyable will cause the reader to prematurely leave the series... sure, it's serious... but no one is 100% serious at all times (and those that are can be great sources of humor by making them have to deal with very odd situations while maintaining their own serious attitude.). It helps the audience empathize with the character and keeps them reading more. There's actually surveys that among college students, 91% of men and 81% of women surveyed said that a good sense of humor was crucial to their ideal romantic partner... a close second to "honesty" and quite critical as a relationship moves forward.