I don't think you can do dungeon raids on those jobs, and without straying into NDA territory, some of the level locked quests in Gridania do require fights. It may not be the same in other cities, though.
You're good, it's been said in interviews with both Yoshida and in the press releaces.
Yes, you will need to level a Deciple of War or Deciple of Magic to advance in the main story at all. Could you potentially neglect the main story and focus solely on crafting? Sure, I bet you could make quite a bit of Gil focusing on the markets that way too.
But you won't be able to participate in any of the primary plot with just a DoL, DoH class.