You can Clock In/Out and Check-In/Out from the same Clock-In/Out and Check-In/Out page when offline. The Check In/Out details are saved and posted in Salesforce once the device is connected with a proper data connectivity.

Known Issue:

You cannot Check In/Out for Travel/Job from Everyone/Users page when you are Offline. Check Ins or Check Outs made from Everyone/Users page are not saved when you are offline.
So we suggest you use only My Team or Check In/Out page for Check In/Out when you are offline.