What happens to existing invoices when I get someone to agree to a pre-approval

When a payer agrees to a pre-approval but has outstanding invoices, the invoices remain outstanding. They do not automatically collect. The reason for this is we think it would upset your payers too much. 

You can however easily process transactions like this manually by finding the invoice in the back end, selecting the process checkbox and pressing the process button. This is found anywhere you can see payments in a list (customer details screen or payments screen).