In theory what you are saying is correct, however there are some flaws.
the OEM diameter exhaust is 2.25, as mentioned.
what you want is a high flowing 2" exhaust. Great, that's going to bring you right back on par to a stock exhaust, and how much money was spent???
Really, people should not modify their oem exhaust beyond a cat back, for sound reasons. In your case, you shouldn't be modifying your exhaust at all, as you will get NO gains in power, or none that are really worth mentioning.
Exhaust mods beyond sound shouldn't really be done until you start to push some real power.