a larger diameter exhaust system will greatly improve performance.
Not universally true. A larger pipe will slow the flow, reducing the scavenge effect of a tuned exhasust. You must look at the most restrictive cross section of the entire system, which is likely, the CAT.
BTW, my 406 blows quite nicely through a new, stock, single, factory, 1984 GM, Corvette CAT. My (illegal) CAT test pipe sits in a cabinet.
The only input to the ECM is this area is the oxygen sensor, which, as stated above, feeds info back to the ECM for its engine adjustments. Long tubes can be ordered with the bung for fitting it.