Nuh, that really isn't the case. There will be no nuclear war between those 5 Security Council members, because of their political power, economic ties and nuclear capabilities.
If they decide to go have a nuclear war, then the human kind will end. No country will be stupid enough to make such move, what is the point to make such move when 2/3 of your people dead and 90% of the cities gone? in case of a major nuclear attack from any other countries, China doesn't even need to lunch all their nukes back to where it from, they would have sent them to Russia’s major cities to trigger the automatic defensive system, then, every advanced country, any major city would have gone, not even need to face the NMD. I say 50 warheads will do. So, major nuclear powerful countries will not start such war, simple as that.
I have to say the Taiwan issue might trigger a very limited nuclear attack, only if the war is getting out of the hand, China would set off a warhead within Chinese territory only for warning purpose.
Once again, the purpose of the NMD is to prevent a limited (either accidental, unauthorized launches or deliberate) Ballistic Missile attack on U.S soil. The NMD might work for keep out the threats from countries like Iran and Libya or even terrorists.
China has the capability of producing enough U-235 and Pu-239 for 100-150 warhead a year since 1980s, whither those material has been turned to warheads was unknown. Sadly, even Japan has this kind of capability and maintained a large storage of the material. (They can’t have nukes, but their scientists say Japan can have the warheads built in a week or less in war time!)
Anyway, if you guys won’t have the thought to attack China with nukes, you should not worry about China would want to start one neither.