when the thermostat is closed,, coolant recirculates inside the engine until the thermostat opens.. then coolant can flow to the radiator, where you will get a surge of cold coolant into the cooling system, and the thermostat will close again, until all of the coolant eventually gets mixed and thoroughly warmed up,, that is why I would hesitate to say radiator being closed off to airflow when the thermostat is closed makes any difference to warm up time.. I think on many modern cars those shutters are more for air flow than for warmup, but also for keeping the engine hot once warmed up..
sort of like a winterfront on a diesel truck is mostly to prevent overcooling in winter conditions, not to make the engine warm up faster.