Correct. Just would re-emphasize that the "fallout" from a nuclear attack wouldn't be nearly as bad as the hype-machine makes it out to be. The explosions would be massive though. We've seen this during tests.
The other thing... ICBM's have never really been tested. Who's to say how well they even work? My suspicion is that while the American ICBM's most likely function as they should, I wouldn't be the least bit surprised if the Chinese ICBM's had a higher rate of malfunction and you ended up with stray missiles that missed their targets completely.
"Made in China" doesn't inspire the greatest confidence in me, but that's just an opinion. If they can't build a car or an airplane, what makes you believe they can build a perfectly functioning set of ICBM's?
Further.... a little known/ considered fact about nuclear weapons is REACTION EFFICIENCY. Only about 2 pounds of the Uranium/Plutonium in the Hiroshima/Nagasaki bombs actually exploded. The rest fell dormant.
While I believe the US have the technology and experience to improve reaction efficiency, I don't see anything from the Chinese side to lead me to believe the same.
In summary, just because they "have the bomb" doesn't mean they're playing with the same deck that we are. I suspect we outgun the Chinese by quite a large margin.