If they meet early, Tidus won't have Break Damage Limit, so your post would have been inaccurate.

And, no, there is no Initiative Ability Sphere, just a weapon upgrade.
he wont have break limit damage. but his attack would still do more than squalls in the beginning...unless squall somehow draws some high level magic early in the game. squall only does like...200 - 300 some damage in the second disk.