A P0420 on it's own isn't going to have any effect on fuel mileage, and it's not going to put the engine management back into open loop. The sensors that manage the fuel mixture are upstream of the catalyst, so they will continue to function just fine. The O2 sensor behind the catalyst has absolutely nothing to do with how the engine runs.
The only thing that would affect the engine would be a catalyst that was clogged to the point that it increased back pressure, but this would be very noticeable.
In my experience, aftermarket cats are garbage. I have had more customers that I can remember who didn't pass an emissions test, went out and spent a few hundred bucks on an aftermarket cat, only to replace it a few months later with an expensive factory unit.