@18% HP for any Legendary (since they all have a catch rate of 3) is:

Without sleep:

You have a 3.245% chance of capturing it per ball. Thus, you have, statistically, at least a 50% chance of catching it within 22 balls and at least a 95% chance of catching it within 91 balls.

With sleep:

You have a 6.452% chance of capturing it per ball. Thus, you have, statistically, at least a 50% chance of catching it within 11 balls and at least a 95% chance of catching it within 45 balls.

Pheramosa, because I think it catch rate is still the lowest:

Without sleep:

You have a 4.402% chance of capturing it per ball. Thus, you have, statistically, at least a 50% chance of catching it within 16 balls and at least a 95% chance of catching it within 67 balls.

With sleep:

You have a 8.752% chance of capturing it per ball. Thus, you have at least a 50% chance of catching it within 8 balls and at least a 95% chance of catching it within 33 balls.

That is very low. Note that sleep is hard to use because they might wake up.

(I did 18% HP because that is about as close as you may get without false swipe)

It possible, just not as probable...

Source