No, what you post is the complete and final form of the story. Some of these forums here may allow you to discuss unfinished stories -- you could send them to people by e-mail or PM if they volunteer -- but the New Stories are all finished works.
To clarify: What you post as a story has to be a finished story. You can't post works in progress or tasters.
After it's posted, you might find errors in it, or just bits you want to change, and then you can post a revised version, which will replace it.
But you can't post 'draft' versions first, then wait for corrections or comments to roll in, then make cumulative changes. The first version you post has to be finished.
(Actually I don't think people should ever post edited or revised versions unless it's really necessary, because to you it might be just a few commas and letters changed, but the editors can't see it like that, and have to read it as if it's a complete new story. They have enough of those to deal with as it is.)
If your story is going to have more than 1 part you would want to complete 1 full section and submit it even if it's not the whole story. that's what I did with my story. Then you could follow up with other chapters. Here's a link to my stories