Upgrading my HD. Will backing up and restoring transfer my saves for games that are no longer installed?

Hi all - I upgraded from 500 GB to a 1TB in my PS4, but am running up against space limits again and want to upgrade to 2TB. I know that if you download your saves from the cloud or transfer them specifically from USB, that you need the game installed or you will get the ""The Application for this saved data is not installed" error and it won't transfer your save locally. I've played a bunch of games that I no longer have and I'd like to have all saves locally. If I use an external HD to Backup and then Restore to the new HD, does it give the same error, or does it restore the system exactly how it was, including saves for games that are no longer installed? Thanks for any help.