That would be appropriate only if the operating costs were explicitly tied to the hour of service. Otherwise, you are simply looking at overhead expenses shared by all activities of the business. But you would not record overhead as an expense directly. Overhead is made up of specific expenses: perhaps rent, utilities, insurance, and so forth that you would want to record in their own accounts. Only after the fact can you calculate the actual overhead rate that applied. Of course, you can estimate these things in advance for purposes of quotes, but those are not financial transactions.
Regardless, Manager will not automatically apply operating costs upon entry of a sales invoice item.
And while you can set up a unit of service sales as an invoice item for convenience in billing, that does not constitute inventory. Inventory refers to physical goods held for manufacture or sale. You must be able to count it, which of course you cannot do with labor.