I don't think he has much of a chance. The Constitution doesn't say anything about first to invent. It just says Congress has the power to grant limited monopolies to inventors for their discoveries.

Note that even under the old "first to invent" law, you did not ACTUALLY have to be the first person to invent something in order to get the patent. A prior inventor whose invention did not qualify as prior art and who did not apply for a patent would not disqualify the second inventor from getting a patent.

The new "first to file" system still requires that the patentee to be an inventor, and that seems to me to be enough to satisfy the Constitutional requirements.