I think it absolutely is and the whole "only 300 warheads" is also a part of the same structure. The strategic thinking is an old one, where China shows the other powers that it is not a military threat and will "behave" with their nukes unlike other "rogue states" they like to point out such as North Korea, or even Pakistan and India who have in the past worried people in the 90s. Same would apply to potential Iranian nukes (so they must stop them and really anyone else who isn't on their leash).
The truth is the 300 warhead count is from the 2000s and still declared up to around 2010 but more recent estimates are publicly disclosed by the US to be around 600 to 1000. Just based on apparent size and variety of Chinese missiles, the 600 to 1000 count seems to be far more realistic, possibly higher now due to unprecedented levels of threat and the breakdown in relations. Also the escalations happening with India. If it hasn't already been stockpiling for any absolute "worst case scenarios" the CCP certainly is getting to it. The Chinese rumours were talking about (last year and this year) the apparent unwillingness to stockpile significant numbers being attributed to the CCP waiting for next generations of weapons which are soon to be ready or have only become ready recently. There are also other methods of MAD being considered and hedged. The attitude is nuclear weapons, even extremely high yield or small tactical thermonuclear (incl neutron bombs) are "ancient" MAD technologies albeit proven, simple, and reliable. The tone is almost fanboyish when describing how much more capable and superior new generations of weapons are and indeed even non-nuclear MAD. Although there is of course a total absence of evidence and the whole thing is word of mouth rumour spreading.
The nuclear escalation theories are all still built on speculation and conjecture as they range from the very simplistic "you nuke me >0% and I nuke you back 100%" to the escalation chains. I think the true nature of CCP's motivations on their MAD program development relies considers everything and must have redundancies and be fool proof while still holding utility even though the law specifically states otherwise, such as how to respond in case of Indian nuclear attack on PLA positions for example. They obviously need a way to respond and certainly have. The formal posture is now half a century old or older with minimal if any changes. I am confident the US knows better about what the CCP has and how it plans on playing their cards depending on the situation.
As for a SCS war, I doubt the PRC even needs to resort to nukes to make it politically unpalatable for the US. They only need to make the costs prohibitive enough and that is first achieved through US death toll. Although the US does have an appetite for losses and bear them even in recent Middle Eastern wars, if the PLAN can do enough damage, the threat could be more than enough to stop any kinetic action. But you can't rely on one layer of defence and assumption. Say the US miscalculates, CCP would need to meta consider everything and have effective tools and responses for every move and every outcome. But I'm sure it does since it's like 2 hours of work given the intelligence (information) available to the ones in charge.