If two users work on the same file while its not checked out the last
person to save their changes wins. That is a function of how Word
works, not SharePoint. Once the document  has been opened it is totally
under the control of the desktop application.

So no, multiple users should not work on different sections of the same
document simultaneously.

Is the document  saved one file or multiple files, one for each section ?

Sharepoint will just treat each file as a separate single  item so if all
sections are in one physical file then no but if they are in multiple files (by
splitting the word doc into sections) then yes, but this would also be true of
2k3