Hahahaha, no. You wish it was that easy.
Download play cannot sustain the level of play that Pokemon has. It will only work with two games. You need friends who play Pokemon, or multiple systems and multiple compatible games. Besides, where the h*ck would you send it? The player who doesn't have the game will lose the record and the Pokemon would be gone upon system shutdown. It's not that hard to think about.
An alternative is available if you have access to Nintendo WiFi; you could always go on the GTS and acquire one of what you're looking for off the trade market from an anonymous source, but what you will likely get will be competitively inferior if that's what you were hoping for.
You could also use Pokemon bank for the purpose of moving them (that won't evolve them, I assume that is the reason you're asking?) but you've indicated you have only one game so it doesn't matter anyway.