Yes, instead of a generic piece of text that just says attached is your invoice, you can use whatever text you'd like in the outbound email message. There are even fields to dynamically insert text such as the date of the invoice, the ticket number, and the tail number.
So you could write a message that says something like.
Thank you for stopping by /~sender_name~/ on /~ticket_date~/. Attached is a copy of your Invoice /~ticket_number~/.
And the customer will see all of their information in the email. There is a key at the bottom of the page with all of the fields you can add to the email.
You can also add a signature with contact information if you'd like.