The scenario you describe is a hybrid online scenario. The offline app will synchronize at startup, when the user taps a sync button or when a connection is possible and a save button with sync-on-save is tapped. At that point any new data on the server from other users will be downloaded as well.
When the devices are in an area where WiFi or 3G can be used, forget about offline, use a hybrid app and publish it in the appstore to take benefit of the latest enhancements where static data is downloaded to the device.
If you need offline, take another critical look at your process, how you assign data to each user and how to handle synchronization because with offline apps you have no control over timing of synchronization of each device. You need to be really sure that the devices do not corrupt or overwrite data of other users. Or have some procedure in place to handle synchronization conflicts. However, designing your detail process steps with offline apps in mind you help you pinpoint the conflict area's and have your stakeholders make choices.