Normally yes, if you upload a new file to a product, any unexpired download links previously issued for that product would start issuing the new file.
However, if you have set up PDF Stamping for the product, each buyer's original link for a Stamped PDF will always download their original Stamped copy of whatever file was uploaded at the time of their purchase, even if you subsequently update the product's file or reactivate the buyer's link later. Unexpired or reactivated links for Stamped PDFs will work for up to one year after the link was first issued.
If you need to issue a Stamped copy of an updated file, you can go to Manage Buyers > Send Free Download Link/Code to issue the buyer a new link for that file. Note at present that feature will not actually email anything, as we had to disable that function due to abuse by spammers, but you can still copy the link generated there and paste that into a personal message to the recipient.
