As long as the show is not copy protected and both TiVos have active service - yes.
Edit - I see you are upgrading. Do they keep the old TiVo active for a while so you can transfer the shows betwen them? If not you will need to transfer the shows from the S3 to a computer before switching your service and then transfer them to the TP after you switch. They would still need to not be copy protected.
Edit - I see you are upgrading. Do they keep the old TiVo active for a while so you can transfer the shows betwen them? If not you will need to transfer the shows from the S3 to a computer before switching your service and then transfer them to the TP after you switch. They would still need to not be copy protected.