Yes and no...
If your cooling system is up to snuff, the engine should operate close to the thermostat rated temperature. If you are operating 20-30* above that temp, then your cooling system is operating below normal capacity.
Case and point:
My car, when I first got it, car was running at 225* With a 195* thermostat. replaced water pump, still at 225*. Replaced thermostat to 180*, car still ran at 225*, just got there slower. Found out my radiator was pretty much dead. Replaced it. Now my engine NEVER runs above 180*. That has all be verified by using a mechanical gauge. Heck, if the temps are below 50*, I can not even get it to 180*.
Remember, the thermostat regulates water flow to regulate temperature of the engine. The cooling system should have enough capacity to cool the engine at any given temperature. The thermostat basically regulates when the cooling system is allowed to operate at maximum cooling efficiency (not talking about the car moving, just maximum flow of water through the system at a given RPM). If the thermostat is 100% open at 180*, your cooling system should be able to keep the engine at the temp.
In your case, running a 160* thermostat, and still running at 200*, I think you have some minor flow restrictions in your cooling system. Consider a flush, new water pump, or radiator.
Slade