I am almost certain the answer is not just no but is on the level of the underworld freezing over level of no. Congress has forbidden NASA from providing any support for China's space program.
Shortly after NASA landed men on the Moon in 1969, the Soviet Union congratulated NASA for its Moon landing. There was a hidden message in this congratulation: "We monitored your communications. We know that you did land men on the Moon." NASA congratulated China shortly after China successfully landed the Zhurong rover on Mars, with the same implied message.
It takes an hour to prepare for communications between a remote vehicle and a Deep Space Network site. The analog equipment must be tuned to the exact frequency used by the remote vehicle, a bit synchronizer must be set up to recognize the bit encoding protocol used by the remote vehicle, and the frame synchronizer must be set up to use the frame encoding protocol used by the remote vehicle.
NASA knows the Tianwen-1 orbiter downlink frequency, and probably knows the bit encoding and frame synchronization mechanisms as well. NASA would not have congratulated China as quickly as it did if NASA was not monitoring communications from Tianwen-1. Imagine now that ESA comes to NASA with a DSN request for a comm link with a vehicle orbiting Mars that does not match any of the frequency / bit encoding / frame synchronization characteristics of any ESA vehicle orbiting Mars but perfectly matches the characteristics of the Tianwen-1 orbiter. NASA will have no choice: They will have to reject this request.
NASA is not stupid, nor is ESA, nor is China. The scenario invoked in the question will never happen, at least not until the US Congress loosens the restrictions on NASA.