You can leave it on FFA and any toon that loots the corpse for the first time will see any recipe, even if it is BoP and they don't have the profession. Note that only the FIRST toon to check the corpse will see it (but won't be able to loot it if BoP and they don't have the profession). Subsequent toons won't see the BoP recipe unless they have the profession.
For trade-able recipes, every toon will be able to see the recipe (and loot it).