I can confirm that having a Poke Ball miss in Gen I is the same as having it shake zero times in later games.
But I've never, ever heard of using multiple Safari Balls or using an item and attacking in the same turn, and I'm pretty knowledgeable about Gen I glitches. The closest I know is that Brock will always, always use a Full Heal immediately after you inflict any status on his Pokemon. This occurs even if the timing would be illegal, such as in the middle of Bide, or if you move first (he'll move second that turn and still get to use the item).
EDIT: Here:
Throwing a Poke Ball in Gen I:
Zero shakes: "You missed the POKeMON!"
One shake: "Darn! The POKeMON broke free!"
Two shakes: "Aww! It appeared to be caught!"
Three shakes: "Shoot! It was so close too!"
Throwing a Poke Ball in Gen II-IV:
Zero shakes: "Oh no! The POKeMON broke free!"
One shake: "Aww! It appeared to be caught!"
Two shakes: "Aargh! Almost had it!"
Three shakes: "Shoot! It was so close, too!"
Throwing a Poke Ball in Gen V:
Zero shakes/One shake with critical capture: "Oh no! The Pokemon broke free!"
One shake: "Aww! It appeared to be caught!"
Three shakes: "Aargh! Almost had it!"
(*Yep, a Poke Ball will never, ever shake twice in Gen V.)
But I've never, ever heard of using multiple Safari Balls or using an item and attacking in the same turn, and I'm pretty knowledgeable about Gen I glitches. The closest I know is that Brock will always, always use a Full Heal immediately after you inflict any status on his Pokemon. This occurs even if the timing would be illegal, such as in the middle of Bide, or if you move first (he'll move second that turn and still get to use the item).
EDIT: Here:
Throwing a Poke Ball in Gen I:
Zero shakes: "You missed the POKeMON!"
One shake: "Darn! The POKeMON broke free!"
Two shakes: "Aww! It appeared to be caught!"
Three shakes: "Shoot! It was so close too!"
Throwing a Poke Ball in Gen II-IV:
Zero shakes: "Oh no! The POKeMON broke free!"
One shake: "Aww! It appeared to be caught!"
Two shakes: "Aargh! Almost had it!"
Three shakes: "Shoot! It was so close, too!"
Throwing a Poke Ball in Gen V:
Zero shakes/One shake with critical capture: "Oh no! The Pokemon broke free!"
One shake: "Aww! It appeared to be caught!"
Three shakes: "Aargh! Almost had it!"
(*Yep, a Poke Ball will never, ever shake twice in Gen V.)