Not without a lot of work. The TH6320 is wireless to an equipment interface box, which itself is wired to the furnace/heater/heat pump/whatever. The Nest (or any other similar thermostat) would need to wire in the place of the equipment interface box, which is probably in an unsuitable place for a thermostat (like right on the furnace, for example). So this may involve pulling thermostat 24VAC wiring from the furnace to the thermostat mounting point.
Unless, of course, that wiring already exists because of an installation older than this Honeywell unit. In which case the job would be “limited” to removing the interface box and wiring everything correctly.
