At the moment there is no way at all to determine if an invoice has been emailed to a client except for opening each one. It would be great if you can report on invoices including the email status so it can be filtered and sorted on this. Even the API has no indication of this emailed status. This is important when trying to work through invoices and determine if someone has actioned the invoice to the client. To have to open everyone is not feasible. If this can be narrowed down via a report then it provides a starting point.
Agreed that this would be helpful. In the meantime, we are using an Additional Attribute for the sales to note the status of the invoice which is then included as a column in the Sale > View all views.