No, but you could get porygon2 in PTD2, but you have to wait until you could be able to transfer pokemon from PTD to PTD2, and you need the dubious disc to be able to evolve Porygon into Porygon2 in PTD2!
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It is impossible to obtain a Porygon2 without trading. You can get a Porygon and trade it with an Up-Grade or you can get a Porygon2 from the GTS but there is no way to get Porygon2 without trading.
Porygon2 evolves by trading with a Dibious Disc
You have to trade with it holding the dubious disk. This can be done when porygon2 is at any level.
Make porygon2 hold a dubious disk Then trade it in order to evolve
Porygon2 is a 2nd gen pokemon and does not appear in Pokemon Red. That aside, both of Porygon's evolutions occur when you trade it while it holds certain item. Up-Grade for Porygon to Porygon2, and Dubious Disc for Porygon2 to Porygon-Z.