UPDATE to Clarify my post.
DO NOT USE ANY SMTP PLUGINS FOR GODADDY HOSTED WEBSITES.
Godaddy has a closed hosting system.
They do not permit you to send any email from the hosting server to email accounts that are not hosted by GoDaddy. All email sent from their hosting servers is forced to use mail(). You absolutely cannot send form or website admin email via SMTP.
More Details in this thread:
https://wordpress.org/support/topic/not-working-with-gmail?replies=16#post-6683898