Yes, it can if faulty or missing.
Yes!
The vehicle will fail the emissions test.
That depends on the engine and the fuel you've used. If the engine starts burning oil a catalytic converter can fail rapidly. Some fuel additives can also cause a catalytic converter to fail prematurely.
The Catalytic Converter is an emissions control device on your car and can be disabled (illegally). Your car will still have power if it is broken/disabled but will fail emissions.
Your check engine light will come on and you will fail emissions.
The check engine light will illuminate and you will fail an emissions test.
The computer has detected a problem with the emissions controls. Have the computer scanned for trouble codes. Get this fixed, as it can cause other parts to fail, as in, the catalytic converter, O2 sensor.
Either catalytic converter or EGR (exhaust gas recirculation) system issues.
Hard starting, loss of power, poor fuel economy, and you will fail any emissions test.
Yes, the Taurus can run without the catalytic converter--it is not necessarily good for the engine, but disconnecting it will cause it to fail emissions testing. If you've seen the Honda Civics running around smoking like a factory, this is caused by no electrolytic converter. The O2 sensor could be in the exhaust pipe between the manifold and converter.
A catalytic converter could need replacing for a couple of reasons. If your municipality require emissions testing a defective converter could be the source of fail emissions problem but the most common reason that a converter is replace is plugging off the exhaust system lowering the performance of the engine. If your car appears to run properly but lacks power a clogged catalytic converter could be the source of the problem. One of the quickest ways to verify this is an intake manifold vacuum check. If the vacuum reading is low and steady this is an indication of a plugged converter.
A Catalytic Converter can fail if it becomes clogged or poisoned but there is no way of knowing when it is clogged. Replace your Catalytic Converter when it starts to malfunction.