Can I produce a report showing all Overdue Sales Invoices?
Yes you can.
Read this for reference.
The Aged Receivables report in the Reports tab gives you the balance of all customer accounts. But it is not broken down by invoice. If you want individual invoices, the Sales Invoices tab is automatically organized by due date. Export the whole listing and manipulate it as desired in a spreadsheet. Or, drag only over those rows you want, copy, and paste into a spreadsheet.
You can also create a custom report with all the movements of Accounts Receivable (invoices, credit notes, payments and so on) grouped by Customers.