No, the deportation ball starts rolling if and when USCIS/ICE decides to make it start rolling. If they haven't already done something to start it rolling, sending in documents to bring their attention back to the case and force them to make a decision is likely to prompt them to start it rolling. Whereas if some clerk simply administratively closes the case for failure to receive documents by a deadline, it is possible that nobody with the authority to push the deportation ball will look at or care about the case again.