A certified master mechanic shouldn't tell you that a plugged catalytic converter will set a p1456. A p1456 is an evap malfunction. This DTC cannot set because of a plugged catalytic converter. Chances are the vibration you feel at idle is most likely a faulty engine mount, if not more than one.
The Catalyist code will most likely set because of a faulty catalytic converter. It is possible that a plugged secondary o2 sensor signal chamber can cause a p0420 but very unlikely.
The Evap DTC, p1456 is a tank side leak in the evap system. Usually caused by a loose gas cap. But, can be caused by many actual failures in the system. Leaks are one cause of this DTC. It has the potential to be a dangerous situation if you have a leak because this is, after all, part of the fuel/tank system!
You can probably just have the Catalytic converter replaced. However, the p1456 will most likely require diagnostics that only a trained professional with proper equipment can offer. I honestly recommend the dealership for this DTC. They will be able to offer the most reliable and efficient diagnostic for you.