It's more. You get 1-2 frags each 60 draws in every treasure on average. So it's anywhere between 2400-4800 draws used(best and worse case scenario). Edo treasure USED TO have higher itachi drop rate (1-2 every 30~40draws) and was the "cheapest reliable way" of getting multiple itachi frags at once, but it was changed to match other treasures

Additional info which might be helpful:

Now since we have 5 treasures (kage, edo, lol, jin1, jin2) and pulling 60 free draws in a treasure takes ~120days, every 120 days you get 5-10 free frags, provided you dont miss a single free draw. So free draws quite substantially reduce overall time you need to draw all itachi frags.