When processing Classic Automations you can either select the current date or chose to a specific date. There is not an option to select the date in which the email was sent as you would when processing standard campaigns. The reason for this is Mailchimp have not included this in their API that Chimpegration talks to.
It is unlikely that Mailchimp will expand their API to include these extra fields, as they are moving away from Classic Automations, pushing their Customer Journey instead.
It is worth highlighting that Mailchimp's API currently does not support their Customer Journey functionality.
If you wish to import Classic Automations, recording the date an email was sent, you should consider setting up a Scheduled Manage Campaign process, to activate daily, near the end of the day. This should give you a relatively accurate indication of when the email was sent.