Absolutely not! Whether the application is for the SAR, the General Society of Mayflower Descendants, or another lineage society or heritage organization, DO NOT turn in original copies of your records.
There are two reasons for this. First, they’re not required. Second, some societies now scan the documents and shred the packet. Not only will you not get the original documents back, but they’ll end up getting destroyed in the process. Everyone is much better off if you submit a copy.
Better yet, make two. Make a copy of your entire packet to submit and one for your records. This second copy can help you provide a back up if your paperwork gets misplaced. Or it can help you start an application for another society.