What is the purpose of the Send email via Gmail option in the Email settings?
The Send email via Gmail option is only used by Zendesk support addresses that use the Gmail Connector as described in Enabling automatic ticket creation for your Gmail inbox. If you see the text connected to Google Mail listed to the right of an external support address, then your support address is connected via the Gmail Connector.
If you have this option checked, all ticket and system notifications are sent from your Gmail, using Google mail servers instead of Zendesk mail servers. This means that you do not need to set up SPF or DKIM to authorize Zendesk Support to send an email on your behalf because the email is sent directly from your Gmail account. You can find all notifications in the Sent folder in your Gmail account.
Google has sending limits that restrict the number of messages sent per day and the number of recipients per message. If you approach the limit, you will receive a warning and notifications will temporarily be sent from Zendesk mail servers instead of Google mail servers. For more information on Google sending limits, see the article: What does "You've reached your Google sending limit" mean?