Let's say a customer pays for a manual invoice using either a check, ACH or wire transfer, and you record the external payment in Recurly - will this information sync over to QBO?
YES - after you record an external payment on the Recurly invoice, the update will sync over to QBO. The invoice in QBO will be marked as Paid, however, it will not specify how the payment was made.
If you want to ensure that the QBO invoice shows the payment method and any other payment details, such as a confirmation # or check #, for example, then you will need to add that information under the "Note to Customer" section in the Recurly invoice. If you add the details there, this will sync over to the "Message on Invoice" section in the QBO invoice.