Back Off being defy, has the card count been played or not? For the effect "if you played this from your hand, draw 1".

No — you don't draw. A countered spell is removed from the chain without resolving, so none of Back Off's instructions are carried out — including "If you played this from your hand, draw 1."

This matches how Defy works against any spell: countering means the card never resolves (Rule 425.1.a), and a countered card is also not considered "played" for effects that check that (Rule 425.1.b). So even the "played from your hand" condition isn't satisfied — Back Off goes straight to your trash and you get neither the Stun nor the draw.