Yes, theoritically this - Assuming your using Matter as the interface protocol. That said, I think the support for matter T-Stats is fairly limited, setpoints, on/off, mode, and current temps, that's about it.
But you should definitely read the following threads - There is a HE built in Googe Nest Thermostat driver available - But some questions to be considered are:
Hence my comment above about "the technically" are supported, but @bcopeland would have to weigh in on what works, and what's actually exposed on the matter side. - But yes, after provisioning (setup), Matter is all local (so no Google cloud dependancy). The second thread mentioned above, has a good screenshot at the top that shows what the Matter driver exposes.
Regardless, I would just buy 1 and test (with a site with a good return policy), before going "all in", but obviously, YMMV
