If the deterrent isn't at risk, there's no requirement to do the full SIOPS doomsday routine is my point however - they're not accomplishing anything by launching inside that window as the carrier would be lost anyway.That's the problem. They may not have that much time. They wouldn't know whether it was a nuke or conventional warhead and a CVN is a capital asset. It's a totally different scenario to Saddam Hussein launching Scuds. The big question is how far down the nuclear attack warning reaction and decision chain do they get before a US SIOPS response go /no go? Then there are the Russian, Indian and Pakistani responses to a Chinese launch and possible US SIOPS response. It would be a very dangerous and touchy situation.
They may well choose to retaliate on those lines, after some assessment but launching under warning against a limited and point attack which may well not be nuclear doesn't sound likely.
If it were part of a wider action with strikes against the US or US bases overseas, then than might trip the response but I suspect given the disparity in nuclear arsenals, the US can ride out any predicted strike by the Chinese with more than enough of it's deterrent force intact to sit and mull things over for a half hour before working out how much gravel and rubble they're making as a response.