Hey Andy - I used to use this connector extensively. I wrote an initial response here but then I re-read your question.
Your question seems to imply that the reason you want this is to prevent Marketo from sending reminder emails etc for fillouts if the survey is already filled out. This can absolutely be done. Part of the point of the connector is to allow you to take action on surveys being filled out and on individual survey responses.
When the survey is filled out SurveyMonkey sends the answer through the connector in the form of either field data or a custom activity (you choose these days). If you use the custom activities option, which is what I'd always recommend, it gives you a "Filled Out Survey" Filter and Trigger, and you could use it to check if a survey has been filled out to prevent sending emails, reminders etc to take the survey.
If you need my "everything the SurveyMonkey connector does" documentation that I've written just follow me, we can exchange emails and I can send this to you.