Yes but riding with a contact may not always mean the horse is in a frame. When riding with contact you are setting up the frame
Well yes and no, they all depend on each other. By riding in a good contact, the horse is more likely to accept the bit and work through his entire body and achieve a nice frame.
But it doesn't work if the horse is forced into the right shape using his head, he has to work all through his back as well or it's pointless! Hope this helps!