No wait, this is actually a FASCINATING hypothetical to contemplate, even if you put aside the shipper lens. because, when you watch the scene, neither of them decisively won or lost that fight. Both of them lose one sword each, and end up in That Spinshot™ before the Dai Li arrive and say:
And Jet disengages from the fight and says:
"Arrest them. They're firebenders!"
Interesting. Throughout this entire sequence, Jet repeatedly addresses the bystanders, the onlookers, the crowd. The only times he directly addresses Zuko (and Iroh by proxy), is when he's trying to goad him into firebending. Right from the start, it's an intentionally public (albeit rash,) attempt at proving their origins and his claims undeniably, and alerting the milieu and the authorities. Crucially, he is not trying to KILL them HIMSELF. When the Dai Li tells them to stop, HE COMPLIES, probably because he genuinely thought they'd hear him out on what he's damn sure he saw. The Jet we see at the tea-shop fight has not taken it upon himself to personally do away with the fire nationals, but rather prove his claims to the public and make it possible to take collective/official action against them (which again, makes sense in context of his character arc and motivations for going to Ba Sing Se).
And as much as he hates his life here at this point, Zuko is pretty darn serious about not blowing their cover. Sure, he immediately squares up to fight Jet (because he's still Zuko, and working customer service at that) but at no point does he say or do anything that might give them away. He says a total of two lines throughout the whole sequence. Literally relentless force vs immovable object.
Which brings me to why this is so very intriguing in context of the art here. For the fight to have gotten to that point, there had to have been no intervention (the guards didn't seem interested in doing so in the original, and neither did any of the bystanders). Zuko, assumably, still hasn't done anything to prove the accusation. They're, once again assumably, still in public, with a significant audience, at that. Jet literally has 'Lee' pinned at swordpoint. He could kill him right then and there.
But would he? Would Jet, the boy who's trying and failing to do better, considering the juncture in his life that he's at, outright kill the people person he knows suspects is a firebender - finish the job himself for the greater good? And if not, what on earth would he do at this point? What would Zuko do, one arm immobilized, the other gripping the blade itself, facing imminent death for all he knows (unless he does something)? What would Iroh do, Iroh who's been watching and yelling placations from afar?
Anway, sorry for the mini-essay, and i don't know if I was able to put across my thoughts clearly, but I think this situation would be soo interesting considering their individual motivations, where they're at in their lives currently, and how it has affected them.