Hi Jason,
We actually have a Shopify app that does just that. It's called Sufio and it automatically creates PDF invoices for every order in your Shopify store, and then sends them to customers iby email.
http://www.sufio.com/shopify/invoice
The file not part of the order confirmation email that is sent by Shopify, because this email does not allow to attach any files. But our app allows you to create your own email templates for the invoice email.
If you need any help just let me know.
Hope this helps,
Norbert