but it would mean that each of the machines that would be capable of editing the site, would need a complete copy of the site.
I think iWeb uploads the entire site each time there is a change. I'm not 100% on that, I could be wrong.

If you are publishing iWeb to a .Mac account then the problem might arise as to which .Mac account was being used. If it was being published to another server then your idea should work.
BUT. Once machine "A" had edited a page on the site and uploaded it to the server, machine "B" now has an out of date copy of the site. You "may" be able to just edit and upload one page at a time by downloading the page, editing it and uploading it again.

Best way to check this is to make a small site and try it out