Can I unlock without internet connectivity?

Yes, you can. Your keys a locally cached on your phone (7 days per default).

Your keys are automatically refreshed and extended silently in the background as your smartphone has internet connectivity. Usually users do not notice the background refresh process as there is no manual interaction required by the user.

TIP: You can even use your keys in flight mode. In this case, you must first explicitly enable the interfaces (NFC or BLE).