I am not sure if Google uses this to prove which is the original copy. Most website owners don’t know this exists. So it’s hard to use it as proof of the original, because the original creator may not even use the tool.
However, if everyone started to submit key articles, then it theoretically could compare the two fetches and decide which is earlier. It could be automated too with sitemap uploads as you post content.
Moreover, you could then use this as evidence in a DMCA take down that your copy is the earliest. Anyways, there are ways to prove earliest content.