FWIW for jams I generally try to create a project page & upload a “safety” upload at least a day ahead of the deadline. (It’s a good way to ensure you can export+upload+submit+play/download & is a lot less stressful time frame to troubleshoot if you can’t. :) )

And, yes, when you upload an updated version the new version should be available for download or (after you enable it the new upload) for in-browser play. You’ll probably want to hide your older uploads via the game page in your itch.io dashboard.

I normally add a note to the project page that current version is a “Work In Progress” version or similar.

I generally hide the project page from “Search & Browse” until I upload the final version though, so non-Jam people don’t find the WIP version.