The world built by The Hunger Games is a corrupt one full of powerful people scrambling to keep their hold while teenagers are caught in the crossfire. That crossfire, of course, involves an arena battle to the death. It's not exactly the kind of world teenagers from a '90s family show like Saved By The Bell would fit into.
If thrust into that world, however, some of the characters would definitely have advantages over others. Athleticism, intelligence, and charm can get a teen far in the games, but they have to have a unique amount of skill and determination to actually win, which not all of the Saved By The Bell characters have.
Screech
Screech is one of the smartest of his friends. He builds a robot that is capable of learning when he's just a sophomore in high school. That being said, Screech also has one of the saddest Saved By The Bell stories since he's often the one left out of group activities, and the one bullied into doing what everyone else wants to do.
In The Hunger Games arena, Screech wouldn't stand a chance. His lack of coordination means he wouldn't pick up on combat skills very quickly. It's likely that if a more hostile tribute didn't get rid of him immediately, a powerful alliance would use him to their advantage, and that would lead to his death.
Lisa
Lisa barely outlasts Screech because she is better at reading people than him, so she has a chance at manipulating others into an alliance. She would survive as long as she had someone to do the dirty work for her.
Though Lisa, as someone from a wealthy family, would likely get some sort of "career" training before she entered the arena, she's not interested in mes her fashionable ensemble or breaking a nail, so she'd only learn the bare minimum. That means she wouldn't be at as much of an advantage as she could be. Lisa definitely makes it through the opening scramble for supplies, and the audience would likely love her, but she wouldn't last more than a day or two in the arena once her allies realized they were doing all of the work.
Mikey
Some Saved By The Bell fans might not recognize Mikey. That's because he was Zack's best friend back when the series was still Good Morning, Miss Bliss. The audience doesn't get to know him quite as well as other characters since it only lasted a single season, but what they do know is that he's a bit of a hot-head who tends to bite off more than he can chew, but he's also afraid to speak up until he's betrayed by one of his friends.
Mikey likely wouldn't survive the opening of the games as a result. He would think he could grab a weapon or food before anyone noticed, but he'd be wrong. He's someone who would make a run for supplies that someone bigger and stronger would also go after. It would cost him before he even got the chance to play.
Tori
During the senior year of Saved By The Bell, a new student ed the fray while Jessie and Kelly were out of the picture. Tori is a little tougher than the other two, but she doesn't outlast either of them simply because she wouldn't be the best at forming alliances, which would be a necessity.
While all of the friends in the show are seen participating in team sports, making other friends, and pulling pranks, Tori's time on the show is limited and she doesn't appear to be able to do that outside of Zack, Slater, and Lisa. She doesn't engage much with other students, which means she might not be willing to reach out and form alliances that would help her. If Tori tried to get through the games completely alone, she wouldn't last long.
Kelly
Kelly is the stereotypical girl next door. She's sweet, athletic, helps her family out of tough spots, and develops feelings for the school troublemaker. While some of Kelly's Saved By The Bell storylines might not always make sense, there's one thing that remains consistent about her: she's too nice.
Kelly wants to be friends with everyone. She has difficulty lying to people. While she can help pull pranks to get back at people, there's not a vicious bone in her body. The idea of having to eliminate her fellow teenagers would be something she just couldn't stomach. Kelly would likely make it a decent way though the games though, simply because other people like her so much. Sponsors from the audience would send her gifts and other tributes would want her in their group for those rewards. Beyond that, however, she wouldn't make it to the end.
Nikki
Like Mikey, Nikki doesn't attend Bayside High School with most of the main characters. Instead, she attends middle school with Zack, Lisa, and Screech in Good Morning, Miss Bliss. Nikki lasts a little bit longer than her classmates simply because of her competitive spirit. She cannot stand to be on the losing side of any situation, even a brutal one like the games.
Nikki is also much more athletic than most of her friends and is the star pitcher of the boys baseball team. Despite that athleticism and competitive spirit, however, Nikki doesn't like to hurt living things. She also gets grossed out easily, so she would likely try to avoid the violence by hiding out in the arena until she had no choice but to fight, which could work for a while.
Slater
Slater has a bit of an advantage over a lot of his friends; he's not afraid of confrontation. Slater, used to moving around a lot because of his father's job, doesn't hesitate to push back when someone challenges him. That could definitely intimidate enough of the other tributes that they would initially steer clear of him in the arena.
Slater also has wrestling experience, giving him at least some measure of defending himself and experience with hand-to-hand combat. He isn't, however, quite as adept at reading people as others, and he's definitely not as crafty with schemes, which means that while he would make it pretty far, he's unlikely to win.
Stacy
Stacy only appears in a stretch of summer episodes when everyone found jobs at the Malibu Sands resort. As the daughter of the owner, Stacy has a wealthy enough background that she would likely be from one of the districts close to the Capitol in the world of The Hunger Games.
As her time on the show demonstrates, Stacy isn't afraid of hard work, and she knows how to rally people around her. That means not only would she commit to her training (especially for her father, since she wants to make him proud), but she'd also be capable of forming an alliance pretty quickly. Stacy would likely have a handful of people she meets during training on her side, allowing her to make it almost to the end of the games.
Zack
As the star of the ensemble, the audience gets to know Zack better than anyone. While Zack can be a great friend in Saved By The Bell, he can also be incredibly selfish. In some years, that desire to be the one on top can be enough to win.
Zack is charming enough to have audience sponsors on his side and to trick people into allying with him that he would likely abandon to save his own skin. He isn't callous, and the death and destruction in the games would certainly get to him, but he would make it nearly to the end without ever having to get his own hands dirty because he's just that adept at getting people to believe in him.
Jessie
While it's no secret that Jessie allows academic pressure to get to her in Saved By The Bell, she's also an incredibly fast learner, able to adapt to situations she doesn't like, and is just as athletic as Slater. Jessie would also be aware that she would have to work incredibly hard to keep herself alive because the Capitol would put a target on her back.
She is the one character who constantly wants to see things be fair, to see her male and female classmates on equal footing, and who highlights the horrible things that have happened in history. Jessie would call out the games for the barbaric practice they were, but she wouldn't stand down in the arena either. Jessie would win it all and try to dismantle the entire institution.