Hi David,
Yep its possible and its pretty easy in NAV 2013.
A brief Idea how you can do it -
1) Specify the path in Some setup for Saving PDF Format of Report.
2) Create a report to set option, Set Filter and Save it in PDF.
3) Same report can be used to create a E-mail message as per requirement.
4) USE NAS to run the new Report Created to automate the process.
I Hope you will be able to do it easily. Let me know if you have any issues.