Agree with Peter Aawen, and others that changing the exhaust system changes the engine operating dynamics. The OEM has programmed the ECU to use engine parameters and ancillary component influences (exhaust system being one of these) to meet emission standards and to deliver the correct amount of fuel to achieve the correct air-fuel mixture at all times, it's a package deal. The OEM has delivered a product that is the best compromise for every day operation. Engine timing, dwell settings and the likes are used as well. We have no idea what is inside that black box.
The short answer that I can give is that an exhaust system change can result in a fuel rich - fuel lean condition, or both depending on the new exhaust system design, but now for a short story.
Changing the exhaust system changes the exhaust system exhaust flow harmonics, these go back and forth in the exhaust piping affecting the back pressure on the engine, affecting the manifold air pressure, affecting the pressure differential across the fuel injectors, affects the fuel rail pressure, affecting the amount of fuel being injected into the engine at any given time. This can cause the engine to operate in a fuel rich - fuel lean condition to varying degrees that the ECU cannot compensate for because the ECU does not monitor exhaust system dynamics. O2 sensor readings affect the ECU fuel calculation, but this is always an after the fact impact. No one sensor can 100% compensate for an aftermarket change.
O2 sensor(s) are used in the "closed loop" operation (generally at idle and low engine powers), and are normally in the "open loop" operation at higher powers and do not affect the ECU fuel calculations. A good book to read on this is Stealing Speed by Max Oxley.
The good news is that an EFI system can be calibrated to accept the new exhaust system if you have access to the ECU programming and the programming can be adjusted to bring everything back into line so to speak. If you do not have access to ECU programming, sometimes best to leave as is, but if you do make a change, nice to know what effect it may have on the engine.
We pay a lot of money for our "toys". Aftermarket additions are great, fulfill a personal need to make a product our own, but one has to wonder how the product was designed and tested. I did the same with my '85 Honda Gold Wing FI model. Changed the fuel injectors for a set from an '85 Honda Prelude. Different size, smaller. Injector data is different than the OEM originals. Engine appeared to work well, or did it?
Had the OEM fuel injectors cleaned, flow and leak tested at different shops. One shop indicated an injector flow rate of 280 cc/min, the other 315 cc/min, huge difference. No issues with the fuel injectors using the OEM ECU - OEM system designed to use these, huge difference with the aftermarket DIY ECU. Had the 315 cc/min fuel injector data for the aftermarket DIY ECU, made a difference in being able to start tuning the engine. Think the 315 cc/min is the true flow rate.
Was fouling the plugs on my '85 Honda Gold Wing FI model with the new aftermarket DIY ECU. Found out there are no less than four fuel enrichment percentages used that augment the amount of fuel being delivered to the engine before the engine reaches normal operating temperature. Go figure.
How do I know about this? I am changing the OEM ECU to an aftermarket DIY ECU for my '85 Honda Gold Wing FI model. There is no information regarding the OEM ECU programming, and there are no shops that can do any changes to the OEM ECU.
I like making changes, doing modifications to make my "toys" my own, and would never say not to do so. In mentioning this, the better informed I am, the easier the decision process.
Short story and hope it helps. Nothing is ever simple. Cheers