Hi there, tjconsultants10-. 

Thank you for reaching out to the Community. Yes, you can import past paid invoices in the system. However, we're unable to mark paid invoices without receiving payments. To import invoices in QuickBooks Online, you can refer to this article: Import multiple invoices at once. 

Also, I am adding additional reference on how to record invoice payment in QuickBooks Online. 

Fill me in if you need anything else. I'll be more than happy to help you. Have a lovely day!