Oh no doubt Byakuya can make things difficult with shunpo and kido and crap, especially if he keeps it ranged, possibly to the point of actually defeating him even with the eyepatch off depending on how it plays out. You see the thing is, that's not how Byakuya fights. At least not in the beginning. Byakuya starts off keeping it a close range fight, which is Kenpachi territory. If he manages to take advantage of that before Byakuya can get a guess as to his actual skill level, it's certainly possible for him to get a few hits in, and perhaps if he's lucky defeat him early, even if that's not how shonen works.
You see, that's why this falls down to the person writing it and in general opinion on these things, which I stressed earlier, which is why I can buy this fight as it played out, provided they didn't have knowledge of his strength and style previously, which they didn't. As long as literally wrong things aren't thrown in, like him being faster than Byakuya or more importantly Soifon, or just him powering through Byakuya's bankai without his kendo (x3<x5-10) and effortlessly defeating him, it's certainly plausible. You might not agree with it sure, due to your own opinions on the events of canon, but it can't just be written off entirely.
As I said before, the scenario heavily favored Kenpachi to say the least, and him pulling the same thing ever again (Barring psychological issues resulting from how damn scary he is and the fact that he almost killed them which I doubt would be the case with this bunch) is utterly impossible.
Timeline is much the same deal, falling to opinion, though given the scope of canon Heathen had, I'd say it's a decent enough guess.