I installed the game on both iPad and Android tablet, and the answer is: No, you can't synchronize between platforms.
The long answer is that synchronization would require you to log on a device independent server (e.g. from Obsidian, or Facebook, or Google) with a username and password, so that your game information could be stored there and loaded on the other device when you log in with the same username and password. But the iPad version only stores data on Gamecenter, and the Android version only stores it on GooglePlayGames. Those aren't compatible with each other.
I have an untested theory that the way the game saves would at least make it possible to not lose your game progress when you switch e.g. from an old iPad to a newer model.