Editing Customers “on-the-fly” is available. When you in an Order in OE, there is a Customer button.

Click the Customer button and the user is in View mode for the Customer.
There is an Edit button that allows us to modify/update the record.

However, note that when you click OK on the Customer screen, the modifications are saved, yet the current Order does not pick up the update.
(At least I have not been able to figure out how to update, for example, the Customer Address on the BillTo/ShipTo tab by updating only the Customer profile. It appears that updates done to the Customer are saved for next time that you access the Customer record. If you need the current OE Order updated also, you have to do it in the Order that you are working on, or cancel the Order and start over.)