By default, outbound email notifications are sent from Zendesk's servers. However, if the Send email via Gmail setting is enabled (Admin icon () > Channels > Email), outbound notifications are sent directly from the Gmail account that you've configured as a support address.
This applies only to tickets that were received at an external support address connected via the Gmail Connector.
It is possible to check the Sent folder in the Gmail account used for the email in question. If your Gmail account indicates the message was successfully sent, but the recipient did not receive it, share the message ID in the email header with the recipient's email admins for investigation.