Not even. Only one Zumwalt of the two active (third one is not in service yet) is currently being refitted for CPS missiles. At-sea testing is still 2-3 years away, so realistically even this one refitted ship won't reenter operational service until 2028/2029. Regardless of that, the main issue here is how abhorrently expensive it is. The land-based version, LRHW, is $43M(!) per shot. I still wonder how. A ship/sub-launched one is even more complex and will cost more.
If we assume say $47M per CPS missile, and a Zumwalt/Blk 5 Virginia can carry a maximum of 12 CPS missiles, that means to just launch all of those, would cost over $560M (!!) just to launch all twelve. That's the cost of a single Type 052D DDG. Add in two for 24 missiles, that would be well over a $1B dollars. An entire Type 055 would be cheaper to purchase which can carry anywhere from 32-40+ YJ-17/YJ-20/YJ-HCM that all have long ranges. Let's say you launch 24, and assume even a "low" interception rate of say 70%, that means only 16-17 of that 24 get through to their targets. So you just spent over $1B USD to just hit a few targets. You better hope that whatever you're targeting is extremely high value and will benefit your goals in the short/long term.
It simply isn't sustainable and why I think its not that potent of a weapon even if it is good. Like you said, hypersonic munitions will only be expensive niche capabilities for the US rather than them being critical and main weapons that play a much broader role in China's doctrine and tactics of their use.