When you upload a document it becomes the default template to that specific board and for all newly created items on that board. Any existing items that have not yet started the signing process will also use this new template when you delete the old one and upload a new document.
However, any items that have already started or completed the signing process will keep the original document as their template. So if you delete the original template, these completed items will still have the old document as their template, while new or in-progress items will use the new one.