No, your friend is no longer an Indian citizen therefore should not be attempting to travel on an Indian passport under any circumstances. This can cause problems later if your friend applies for OCI and the Indian govt finds out about illegal use of Indian passport. I don't think the US govt would approve either because your friend would be traveling with false travel documents.
Your friend should go to the nearest US passport center and apply for an expedited passport which can be gotten in a day if you can prove the emergency. Next your friend needs to apply for a India visitor visa at the nearest consulate, again proving the emergency to get it done in day.