Can version control systems, like Git, be used to establish priority date of a paper?
I understand your question in the following way:

You are asking if a git repository can be used to add a "timestamp" to some idea, so that in case multiple researchers come with the same idea, you can prove that you were the first (whenever this is actually true).

Unfortunately, dates in a git repository can easily be forged. See here for a stackexchange thread documenting this.