The device wouldn't be directly influencing connection. If it is an older device with slower parts, it may have trouble running the game, but that has nothing to do with connection. Similar to a computer, nearly every computer as the wifi connection to play Crysis 2 online. Still, only a small percentage of those computers have the actual computing parts to run the game properly.
So, if an iPod 2 appears laggy, that may just be because it doesn't have as good parts as an iPod 4 would, very unlikely that internet connection has a hand in it.