No. What happens is the group member who clicks on 'submit' first will get all their changes saved. When the other person clicks 'submit' they get a warning that changes have been made since they began editing the document. This warning tells you that clicking on 'submit' will overwrite the changes made by the other user and do you want to do this? If you should ever see this warning, the etiquette is don't overwite, exit without saving your changes and try again later.

For a group of people planning to work on the same CommunityCentral document it would be a good idea to agree who needs to edit it and when. A handy tip is use the Comment field to manage the process. As each member does their bit, they add another comment to tell everyone where they are up to.