Incorrect and totally erroneous. The United States has a fully functioning Anti-Ballistic Missile Defense Shield; the AEGIS ABM Platform on our crusiers and destroyers via the RIM-161 system.
Additionally, The United States tested our ability to shoot down tactical ballistic missile launches via our Patriot Advanced Capability 3 (PAC-3), which had 100% effectiveness in Operation Iraqi Freedom.
Additionally, we have the THAAD system (Terminal High Altitude Area Defense). The following defense shields guarantees that most of the incoming ballistic missiles that the PRC would be capable of launching would be shut ; considering it will be screened and neutralized by USPACCOM, most if not all would be shot down by USNORCOM,USEUCOM,USCENTCOM, USAFRICOM, and USSOUTHCOM.
During a strategic first strike, most if not all of the military arm of the PRC would be rendered nill. The handfew that would hit US targets would be limited in its scope, considering it even arrives at its intended target.
PRC, on the other hand, would be glassed as per American Nuclear Policy. It would be erased from the face of history.
So yes, this hypothetical war scenario doesn't end well for the PRC.