Can too much back pressure caused by a new.

The reason I asked was because my midpipe cracked. After being replaced I could notice the car sounder a lot louder on the drive home from the shop and planned to take it back to find out why the next day after work. On the way to work the P0420 code popped up, when I got to the shop they scanned the car infront of me and told me I needed a new cat before the next time I got my car inspected without even looking at anything. I've read that exhaust leaks, faultly o2 sensors, and leaky injectors could throw false 420's. The new midpipe installed def looks smaller than the original and with the louder engine noise I was curious if the back pressure could be causing faulty readings.