This is currently isn't possible as marketing emails aren't considered an object record. This is a great suggestion though 🙂I would highly recommend you to submit this as a new feature in the Ideas Forum here.
The HubSpot Sheets Integration is based on an actual individual object record in HubSpot, such as contacts, tickets, deals, or companies. For example, if a ticket is enrolled in a ticket-based workflow, the fields for that ticket record will be sent across to a Google Sheet.
I would also like to invite our subject matter experts to see if they have any ideas about how you could automatically send marketing email metrics to an external doc or system.