Is it possible to include additional contacts to receive the email notification when a document is signed by recipient?

Yes, you can add up to (5) additional email addresses by modifying the email alert that comes with the installed package.
Go to Setup > Workflow & Approvals > Email Alerts > Click “Edit” to left of “Email to document owner” and then you can can enter up to five (5) email addresses to be notified. This option will add them to the email notification (with link back to eSign doc record) though the signed PDF is not included.