Yes, you can run atVenu Register and collect Credit Cards while offline using Offline Mode.
Transactions that occur while in Offline Mode will be stored on the device until an internet connection is restored. At that time, the stored transactions will be processed.
Offline transactions may get declined by the bank when processed. You are responsible for all declined transactions. Please ensure you get back online as soon as possible, to ensure you can verify that charges are valid.
Also see the article: How do I setup atVenu Register to accept offline payments?