No…The downstream sensor is simply monitoring the efficiency of the CAT…
The “hesitation” you describe is probably misfire of some sort that is not profound enough to set a fault code of it’s own…But the misfire sends too much unburned fuel into the exhaust system for the converter to handle so it throws a code…But even THAT is suspect, because the code was for the sensor heater circuit, which is not related to a engine performance problem. So the hesitation and the CEL are probably two separate issues…
You can try to force the issue by doing a few full-throttle acceleration sprints which should bring the misfire problem to the attention of the ECM and perhaps a code related to the problem will be set…
Something you can do yourself, clean the throttle body and mass airflow sensor and the PCV system. Replace the air filter if it’s dirty and inspect the intake path for any debris…next comes spark plugs and valve adjustment, if applicable…