Unlikely. Israel, a nuclear power by 1973, was attacked by multiple countries, and did not launch nukes. Russia, another nuclear power, is receiving attacks from Ukraine on a daily basis, and is not launching nukes.

As much as nuclear powers want you to think they will use them if you resist their goals, nukes only come into play when state survival is at risk, not when belligerents pursue limited goals. The US will never pursue the defeat of China. They will manage escalation. They will pursue the limited goals of status quo maintenance and a quick resolution, which can include bombing industrial production nodes to signal that China will lose a war of attrition, forcing it to call off an attack on Taiwan.