Short answer
The "Publish to the web" feature of Google Documents doesn't include an option to add the link to edit the source document so one of the several ways to add the link like Google Apps Script and Google Documents add-on, Google Sites Gadget, JavaScript, etc. should be used.
Extended answer
Since the URL to edit a document has the file ID than the published to the web URL there are lot of ways to add the a link to edit the document at the bottom.
URL of a published to the web Google Document:
https://docs.google.com/document/d/1ZyU97pNm0wDtOziWKnToUnjtAZarpnny_8eohF8-_F0/pub
URL given by the Share feature:
https://docs.google.com/document/d/1ZyU97pNm0wDtOziWKnToUnjtAZarpnny_8eohF8-_F0/edit?usp=sharing
URL given by the Google Drive get a link feature and getUrl() method:
https://docs.google.com/open?id=1ZyU97pNm0wDtOziWKnToUnjtAZarpnny_8eohF8-_F0
File ID
1ZyU97pNm0wDtOziWKnToUnjtAZarpnny_8eohF8-_F0
Considering the above, in certain scenarios could be easier to add the link manually than to automate this task.
Example
The following Google Apps Script snippet adds the URL of the document at the end of it's body.
function appendUrl() {
var doc = DocumentApp.getActiveDocument();
var body = doc.getBody();
var text = 'Edit this document';
var url = doc.getUrl();
body.appendParagraph(text).setLinkUrl(url);
}
The above is the same than copying the URL of the document and insert an hyperlink at the end of the document.
References