Does Siegebreaker need an internet connection?

No. It plays anywhere. Only buying the full game, and checking that you own it, needs Google Play.

No. Siegebreaker plays without a connection, in airplane mode, on a train, or anywhere the signal drops. The Daily Siege works offline too.

The only service the game talks to is Google Play, and only for the full game: to show you its price, to make the purchase, and to check whether your Google account owns it. The game remembers the answer, so once the full game is unlocked it stays unlocked offline.