One thing to consider is the state of the gAang at the time. If Zuko arrives immediately post-Day of the Black Sun, I think he'll have an even harder time of it. They've just come off of a colossal loss on their side, losing parents and adults to the Fire Nation prisons. Sokka was played like a fiddle by Azula, emotionally toyed with about the fact that his main squeeze is a prisoner and possibly gave up on him coming to help her. They are going to be at an emotional low point.
Now here comes Zuko, not only the Prince, but the guy who had doggedly chased them through the winter. He's kicked Katara's butt on one occasion, dragged Aang out into a blizzard, wrecked a lot of places he's chased them to (Southern Water Tribe, Kyoshi Village), and was somewhat responsible for Aang's injuries and the fall of Ba Sing Se. Without Zuko lending his support to Azula, it is very possible Katara and Aang combined would have defeated her (because Katara was doing pretty well on her own), and that could have led to an entirely different outcome. Even with Zuko just sitting it out on the sidelines and not helping Aang they would have ended up better off. He "betrayed" Katara to join psycho sister and that really ruined their "moment."
Showing up so suddenly would cause suspicion at the very least among the group. They will attack him first and ask questions later. Zuko is probably smart enough to only use his abilities to defend himself, or smart enough to not do anything at all. I'd suspect that they'd want Toph to use her lie detector abilities on him, but be wary whether it works on him (since Azula was so good she could bypass it). They'd probably make him tell a blatant lie as truthfully as possible to get a gauge. Zuko's a pretty lame liar, so that might help him in the long run.
Having said all that, I'm thinking that absolutely no one in the group will want to see Zuko at all.They will be openly hostile to him, and not trust him in the absolute least. After all, he could be a spy sent by Azula, right? Or he's working on his own to gain their trust only to hand Aang over to the Fire Lord at the very last minute. This is pretty much what I think the attitudes of the gAang will be when Zuko first approaches them:
Toph: she has the least personal grudge against Zuko, but that doesn't 'make it any easier. The others have told her how Zuko has pursued them for months on end, she's well acquainted with his sister and her brand of evil, and is probably pissed that he betrayed Uncle Iroh at Ba Sing Se, keeping in mind that Toph considers Iroh a friend of hers. That said, she is aware that Uncle Iroh had said his nephew was "lost," and both have an independent streak to them. Eventually, she'll probably give Zuko some nickname (hothead, adopting Sokka's angry jerk name, whatever), and they could have a good friendship. But at first she's gonna be all kinds of suspicious. Oh, and she has met Zuko in person once before, at the end of the Chase. Then Azula injured Iroh, Zuko threw a fit and drove them away.
Aang: He is emotionally in a bad spot right now. There's still some ambiguity with his relationship with Katara, and he suffered a bad loss at the Invasion. This could mean he'll be more surly and suspicious than usual. After all, Aang has offered Zuko friendship before, but it had been thrown right back at him. The two have come to blows so many times that it's hard to let all that go. What helps Zuko's case is the lesson Roku imparted to him, and that Zuko has gotten a hold of the royal artifact that Roku wore. He could possibly be the easiest to win over, but Zuko still will have a lot of explaining to do. And if Zuko ever looks at Katara, it could spark that jealous streak Aang showed in Ba Sing Se. Even if Zuko means absolutely nothing by it. Once they work past the trust issue, there could be some awesome comedic moments with Aang learning firebending.
Sokka: I can see him either being easier or more difficult. Sokka has arguably held the hardest grudge against the Fire Nation from the beginning, and can be suspicious as all get out. He's very aware of all of Zuko's misdeeds, and told Iroh he didn't want to help Zuko until he had good "on the outside as well." He could be feeling very antagonistic after his encounter with Azula and take it out on Zuko. If Zuko doesn't strike back, I think it'd bode better for him. Odds are, Sokka will take a long while to win over. He will follow his instincts (which do tend to lead him right a good deal of the time), and watch Zuko like a hawk (but not Hawkey
). If Zuko could potentially help Sokka bust Suki out of prison, or perform some sort of act of sacrifice for the gAang, I can see Sokka letting go of the grudge to the point where they could be teammates. Personally, I would love to see them work as partners, like buddy cops, with their swords to kick some serious tail. The show has made a few parallels between the two (though not as much as Aang and Zuko), so the two definitely have some things in common. Just seeing Sokka use his sarcastic wit on Zuko would be hilarious. Zuko could prove his usefulness by tipping off a possible use for Sokka's White Lotus Tile.
Katara: She will be the hardest to win over, feeling personally betrayed by Zuko and witnessing first hand Aang's 'death.' Katara can hold grudges probably just as good as her brother, and when you mix in anger at Zuko as a person and not just as "Fire Nation Prince" you've got a recipe for some bad juju. She will be fast to attack him, freeze him, shoot water at him, smack him around on a regular basis, what have you. Zuko will need to not just explain himself, but be calm, self-sacrificing, and a team player to even get Katara to ease up.
One other factor that could help win their trust is Appa. Although Appa is well aware of all the bad stuff Zuko has done, the last time he really saw him was when Zuko released him from the Dai Li's dungeon under Lake Laogai. I doubt that Appa will forget that act of kindness, in comparison to him witnessing Azula's assault on Suki and the Kyoshi Warriors. Appa might even lick Zuko as a belated 'thank you' for what he did. This should be not only hilarious, but cause the gAang to stop and think about things for a moment. Possibly long enough for Zuko to explain himself.
Only one other thing hurts Zuko's chances with the gAang: Combustion Man. In true Zuko Bad Luck fashion, I'm pegging him to show up after Zuko's earned a good deal of trust from the gAang. He will then have to explain that yes, he hired an assassin but that was back when he was stupid and bad, and he's oh so very sorry. Much drama will be had.
No matter what, I find Zuko joining the gAang to be a situation full of awkward hilarity and drama. I really look forward to it and I do peg Zuko to teach firebending to Aang at one point. The guy is now good enough to redirect lightning back at the "baddest guy on the planet" and that has to count for something.
). If Zuko could potentially help Sokka bust Suki out of prison, or perform some sort of act of sacrifice for the gAang, I can see Sokka letting go of the grudge to the point where they could be teammates. Personally, I would love to see them work as partners, like buddy cops, with their swords to kick some serious tail. The show has made a few parallels between the two (though not as much as Aang and Zuko), so the two definitely have some things in common. Just seeing Sokka use his sarcastic wit on Zuko would be hilarious. Zuko could prove his usefulness by tipping off a possible use for Sokka's White Lotus Tile.