I believe you have to create a minimum of 2 inventory organizations. One for Item Master to hold item definitions and second for transactions.
Once you have created the Inventory Organization then you must define Sub-inventories (under those inv orgs) for transactions. For example, upon receiving items from supplier they are inspected and then transferred to the warehouse (which could be your sub-inventory within the inv org),
Locators, Serial Control and Lot Control are optional setups in Inventory.
Its best to consult with Oracle's License Sales Rep to get a clear idea on how much of 'shared' inventory functionality one can use while implementing PO, AP and GL.
You must create inventory organization. Accounts are defined at this level and these accounts will be used accounting entry generation at transaction like receipt, PO Creation (if budgeting is used) etc.....
Yes you should have inventory organization in place however you no need of detail inventory setups like subinventory, locators etc. Based on your business (if it is service industry) you can have purchasing based on category so item is required and all your receipts are expense so no sub-inventory required. As you mentioned they only need to receipts, even though purchasing at operating unit level but receipts are at inventory org level so with your one master inventory you have child inv organization for the purchasing activity.
Hope it may give some highlights.