As above, yes. The thermostat is designed to cycle open and closed. The coolant circulates around the engine absorbing heat until it reaches the opening point on the thermostat. The coolant is then allowed to flow out of the engine outlet to the radiator to be cooled. The coolant that was being cooled in the radiator flows into the engine to start absorbing the heat from the engine ready for the next transfer/cooling cycle.
Engines have a temperature range in which they get the best performance and economy. Also, things like oil and internal parts to the engine operate and protect better in a certain temp range. If no thermostat is used then that range could take longer to get to or not be acheived at all. In which case performance, economy and engine wear characteristics could suffer.
Cheers