Is it possible to mark a record (formula checkbox) when it has been 'saved as spreadsheet'?

Rather than allowing users to natively save as a spreadsheet, you can give them an icon/button to download. It would essentially be a url link to a report where the format of the report is set to csv. 

So prior to directing them to the URL, you can make an api add record call and log that info in a field which puts a timestamp and user info. And you formula checkbox can be driven off that field.