Office 365 will synchronise your calendar to your iPhone but it won't synchronise shared calendars or public calendars in the same way.
However, is it possible to synchronise public calendars and shared-mailbox calendars with your own personal calendar? If this is possible then it will enable staff who are on the road to see the contents of shared and public calendars simply by seeing them in their own calendar on their iPhone.
Does this make sense?
Is it possible?