Does the completed form automatically get emailed to the person who completes it?

Yes it is possible to achieve your requirement by adding "Form Autoresponder" email alert in form which will send an email to the user who submitted form. 

You may like to take a look at the following guide which should help you how to add form autoresponder email alert:  https://www.jotform.com/help/26-Setting-up-an-Autoresponder-Email 

Hope this helps.

Do get back to us if you have any questions.