No you cannot get this information from the item. You will need a separate database to give you this information. If you use the web, wowhead is a good source. If you want an addon that can tell you whether a mob drops an item that starts a quest you can use Wholly and Grail. Together they can do that. However, they can only tell you if mobs drop items that start quests (and not other general items). They do this in a few ways, including in the tooltip of the mob.