If you publish a story, all existing chapters will be published as well. If you want to prevent that, you could save these chapters offline before publishing.
I'd recommend posting single chapters rather often in the first week as long as the story has the "new" badge. (Frequency might depends on how many chapters you already have)
After that, I'd go for regular updates depending on your writing speed.
If you want to ensure the highest amount of possible quality, withhold whatever instance of the story you are currently working on until it is finished and you re-read it to make sure its internally consistent/properly foreshadows.
As much as I like the general idea, I don't think that it generally improves quality.
I've read several deep stories which had a really great beginning but got worse gradually because of getting unplausible. If the author gets that information earlier, they might consider that.
If the author overlooks some inconsistencies even after reading it several times and they happen early in the story, they would have to change half of the story to correct them. I think most authors wouldn't go that extra mile and rather practice handwaving.
Making notes about your character and/or the recent course of action helps to keep track of everything. And re-reading before publishing a chapter should go without saying.
