Can you play Summoner Wars with only the Second Summoner packs?
You can use cards from just the Second Summoner deck without mixing them in with the original faction decks. In fact, this is how my wife and I play; we keep each deck in its original form rather than deckbuilding. If you look at the descriptions for the packs on Plaid Hat Games website (emphasis mine):


  This Second Summoner deck is a full faction deck with its own Summoner, set-up card, Champions, Commons, Walls and Event Cards. It requires a Summoner Wars Master Set or Starter Set to play.


The part in bold is what you care about; it's a fully functional deck on its own. The part in italics might be your concern. The reason you need a starter or master set is to get the player boards/mats and the tokens. However, you can buy the board on its own, and you can use anything from pennies to Skittles for wound tokens, so even a base set is sort of optional.