If I have a HTML form with some embedded divs, and after the CSS is applied the sections of the form end up spread all over the page outside of the original <form> boundaries, does/will the form continue to work. What do the HTML specs say about this kind of thing?
Yes, the form will continue to work. CSS positioning does not affect the validity of the HTML. The only concern is usability or clarity. If it is not apparent that an element belongs to the form you might confuse the users. Or, if you position/layer something where it can't be clicked that will cause problems as well.
But HTML and CSS are separate things... the HTML specs have nothing to say in this matter.
As long as the elements are still children of the form tags, nothing will change. The display does not effect the functionality, so it doesn't matter if they do not appear to be in the same area as the form.
However, if you were manipulating the DOM via javascript and moved the elements out of the form, (by outside of the form, I mean that they are no longer child elements of that form, not that they are visually outside), then they wouldn't be submitted with that form anymore.
Positioning has no effect. Nesting of the tags does. All form elements need to be inside the but I think that's the only requirement.