Hi Edward
Not only does this not read like a quick question, but the answer is anything but simple.
There is a cost field for Adagio Invoice items, but it is for informational purposes only.
There is no specific report that passes Adagio Invoices item cost information to the GL from Adagio Invoices. You will have to create one using GridView or Crystal Reports (GridView is a better option). If you create it with the proper layout, it can then be used as a starting point for importing the entry into a GL batch.
If as you suggest the corresponding entries from Payables would be coded to clear the credit side of the accrual entry, that is going to open up a whole can of worms, because it is almost certain that you will have a major reconciliation job each month when the clearing account does not have a zero balance.
Good luck
Steve