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Certainly possible, you would need to
- Have process builder or apex in SFDC that updates some fields on the lead/contact when a case is closed and passes the ID
- Use that person field update to trigger a Marketo email containing the case ID for reference
- Receive the survey responses through a standard Marketo form and write the data to person fields
- Have another flow or apex back in SFDC receive the data and map it from the person object (lead/contact) back onto the case
There may be a more direct route (perhaps using "email to case" functionality to update the case afterwards) but Marketo cannot write to the case object nor can case updates trigger a workflow in Marketo via custom object sync, so those are the main limitations that require work arounds.
Justin Norris | Perkuto