The short answer is, yes this could be done.
The long answer is how to make it work. Order Entry does not have an invoice export but we have solved this for other clients using GridView. Adagio Invoices does have an Invoice Export function. In either case some leg work is going to be required in order to figure out how to make this work with OB 10's system. To the best of my knowledge no one has created an integrtaion.
Best bet to get this done would to to engage the assistance of your Adagio consultant.