I attempted to use a CR2032 with the circuit and, to be honest, i wasnt too sure if it would work. I suspected that something weird would happen when feeding only 3 volts to the 3.3 volt regulator or the vco being too sensitive, etc. However, none of those scenarios came to be true and it worked wonderfully. Although i suspect the output power has gone down, there were no issues and the frequency stayed rather stable.