I have a PS4 save file created with the latest version of Dark Souls III.
Can I install and launch the game from the Dark Souls III: The Fire Fades GOTY Edition disc and load that same save game?
According to comments on this wiki page for DS3 editions, yes, you will be able to continue using saves from the original version on the Fire Fades edition:
You can continue your save in fire fades.
I have both the normal game version and the fire fades edition for ps4 and yes the save files from the normal game works with the fire fades edition.