Not sure if things changed between generations but the 2.0L should get a 2.0" exhaust, yes. Upsizing post-cat to 2.25" does reduce the "pipe friction" for the exhaust gas so no matter what, flow is improved.
I don't think it's worth trying to upsize on a stock-block/head MZR 2.0. Keep in mind the MZR engines only go to ~7k RPM so we're not even in the regime yet where the built K20A boys start to complain about needing 2.25" or 2.5" piping to avoid choking the engine. 10k RPM's + aggressive cams + ITB's is a much higher flowing setup than ours, so if the biggest built K20's are using 2.5" I doubt that you can make use of it here, yet.
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@bmspec Custom aero/suspension design