We literally see Axel fighting in battles against the Organization. Multiple times. I don't think he is going to betray the others. Kairi is too quick to protect him and the hooded figure Saix talks to is too short and muscular to be Lea.
I'm convinced that hooded figure is either Vexen or Ienzo. Ienzo mainly because he has a larger role in KH3 and I can see him "betraying" everybody as the Cloaked Schemer. He wouldn't actually betray the heroes, but rather he'd have discovered something during his research into the data found in Sora and whatever else Ansem the Wise had hidden up his sleeves in the past, and because of his unique position of having been a part of the original Apprentices and also a part of the first Organization, he'd believe is the best person to infiltrate the new Organization. But then it all goes to tits. 8D
Don't forget he was also one of the people who Xemnas sent to Castle Oblivion, meaning he also thought he might be a traitor that needed to be struck down. He's been willing to bring back traitors as seen by Marluxia and Larxene.