Yes, you can play Chrome Valley Customs offline! However, events will not update/be available, and you will be unable to make any in-app purchases.
If you're playing offline, please be sure to go online and open Chrome Valley Customs so your progress is saved. The game should automatically connect to our servers when your device is online.
It is rare, but possible, for your offline progress to be lost if you don't connect to the server. We are unable to recover progress unless it has been synced!