Will OBO do Progress Billings?

Yes, QBO can handle progress invoicing. https://quickbooks.intuit.com/learn-support/en-us/manage-invoices/set-up-and-send-progress-invoices-... as long as your version supports it

Therefore, you will see the estimate status as Closed when it was fully billed by the customer.

You can run the Estimates by Customer reports to check if the estimates that you're making a lot of progress billing are closed.

Let me show you how:

1. Go to the Search icon and then enter "Estimates by Customer".
2. Change the Report period it was created and then Run report.
   

There you can see the status of the estimate.

If you wanted to reopen the estimate and apply it to another customer, you can click the date of the estimate on the report (Estimate by Customer). Change the Customer name and update the status to Pending and then update the appropriate information.