Yes this is possible.
1. Only Global Admins can toggle this option, from the Administration Dashboard. > Click the "Administration" section. > then Click the "Site Settings" icon. Under the General Settings header there is radio button labeled "Enable Post Acceptance Section Submit Notification:" check this box to yes.
2. Now you must make sure there is a contact connected to the application form. To add a contact to an application first you must go to "Setup Application Forms" from the Adminstration Dashboard > Click the application you wish to add a contact to. > Click the "General Information" icon. At the bottom of this screen you will see a button called "Add a Contact" click this button.This allows you to select a key contact for the application process. This is the contact that would receive that notification email. If you do not enter a contact here, then the emails will not be sent.
NOTE: An application Contact must already have a user account set up in order to be added as a contact.