Do you thing that a 1/4 more will give more power 2.50" verse 2.25. In the old days 2" was standard hipo was 2.5 and big blocks were 3". What do you think could the be the lost hp on the ls3 in the SS.
Foot note my zo6 is 3" necks down to 2.5 at muffler the ss cats are 2.25 out and in I think.
Corvette always gets the best power rating for a given engine package, when you look at air intake design, exhaust manifolds, cat volume, pipe sizing, etc.--the sports car gets a "tune" that is optimized to a different set of standards.
A 4-door sedan, even the SS, is not going to get the same tune from the standpoint of product positioning/price point, if nothing else. Other considerations include fuel economy (if the SS did have the same power level as LS3 in Corvette, the FE numbers would probably be lower than they are now), increased noise level with the higher flow exhaust, drivetrain durability with the higher power in a significantly heavier vehicle (SS compared to Corvette), etc. So, they did the next best thing, and tuned the mufflers of the SS to at least make it sound sportier.
Larger pipe size would be a given for an LS7 in the SS, for example--427CI engine pumps more air than 376CI, especially LS7 vs any other normally-aspirated production LS engine. Still, as the hot exhaust gets further away from the engine, it cools, the gas volume is reduced, and the piping size requirement also reduces--in addition to everything else, pipe sizing must also take into account weight, cost, and clearance in the chassis.
If you further consider that the Corvette is basically unrestricted as far as achieving very high speeds, and is capable of running at those speeds for extended periods, the exhaust sizing becomes important for the engine to sustain high output (thus, high air flow levels from engine air intake to exhaust exit), which allows the Corvette to run 175+ out of the box.
The SS, by contrast, is heavier, less aerodynamic, and really not equipped adequately to run at max or high sustained speed for any significant amount of time (smaller brakes, lack of cooler for diff or more effective coolers for other systems).
The SS likely benefits from the comparatively smaller-diameter stock exhaust system, as it is going to produce better torque at the more "normal" speed range (engine RPM) the sedan typically will see in daily use by the average owner.
In any case, exhaust pipe sizing is based on maintaining air flow through the system while meeting certain velocity parameters, which varies greatly by engine size, anticipated operating mode, and, I'm sure, a number of other factors--some already mentioned, and perhaps others I've not even thought about.
To answer you specific question, I think the use of 2.5" pipe WOULD result in more power capability, but only at the higher end of the engine RPM range (combined with appropriate tuning tweaks). I doubt there would be much--if any--real benefit outside of that.