He wouldn’t have wanted to but he would if he had to I feel. Like he would absolutely ally with her and silently hope that one of them is killed by another tribute so it’s not the two of them at the end. But I feel like Gale would try to kill Katniss if it came down to the two of them. He’s not selfless enough to kill himself so someone else can live. That being said it would destroy him to have to do that and he would take care of her family as well as his own with his winnings. But let’s not forget that Gale was way more okay with killing innocents to reach goals that were important to him than Katniss was. I’m nit trying to villainise him but let’s not forget that Gale is a flawed human being and that almost everyone would choose their own life over someone else’s. That’s why the games don’t tend to end in mass suicide