Can we still use Supply Chain Finance if non-Fusion third-party systems are integrated into our procurement and Accounts Payable flow?

It depends on the role of the third-party application. Oracle Fusion must remain your supplier master.

You must maintain approved supplier invoices in Oracle Fusion, and you must initiate supplier payments from Oracle Fusion. As a best practice, approve supplier invoices as quickly as possible after receipt so suppliers can maximize the benefit of early payment.