Your coolant would not cool. It would cycle through the engine, go through the radiator, then back into the engine. With the thermostat there, it keeps coolant in the radiator to cool down then goes through when the thermostat opens.
If you do nothing but city driving, a smaller thermostat wont keep heat down that much IMO. Its usually on the highway where you stay cooler since you are not sitting. Mine barely gets to 180 when I drive to work and I have a 180 tstat. Now when I use the A/C, I can come pretty close to 210 in no time in traffic.
*Cliff notes* Smack yourself in the head for thinking of running with no tstat. :lolsign: