Well, been hearing this alot, but there are no affirmative action on both side.
Theoritically, it will not ends in war, because the only way Chinese can survive a war with the US is to use nuclear weapon, which is not surviving at all. As I said, US have way too many asset around China, which they can deal blows to China whether or not US winning a war is not in its question itself, China, even if somehow can resist the US invasion (had there been one) China would have pay dearly for the price.
On the other hand, it's not up to China to decide whether or not to "engage" the US like you said, as China have no initiative, there are no way China can make the 64 + days tran-pacific journey without going into either Alaska or Hawaii. That mean if any engagement between China and US are going to happen, it's either China engage a third country (Japan, Taiwan), which US can still choose whether or not they will be a part of this conflict, or US decided to take the initiative and engage China for any reason (Island in SCS, Hainan or Senkaku's or etc) China at this stage, or near future, would be in defensive, not on offensive.
I am not saying a war can or cannot happen, I am simply saying that what you think is incorrect, if war did happen, you cannot simply scare the US away or the American is like a coward you describing, they will fight you to the end. WE saw that before, we are going to see it again.