Let's make this more clear, shall we? Let's use my good old friend called math.

It's different for generation. I will do these calculations based on a Mewtwo with 100% health and no status ailments, with a Master Ball, whose rate is *255x*.

Generation 1's Master Ball is automatically caught. There are no formulas using for a ball catch rate if a Master Ball is used. It bypasses the formula.

Generation 2 uses this formula:

a = (3 × HPmax - 2 × HPcurrent) × (rate × bonusball) / (3 × HPmax) + bonusstatus

Now, let's plug in:

a = (3 x 416 - 2 x 416) x (3 x 255) / (3 x 416) + 0

Since 3 x 416 and 2 x 416 are both greater than 225, the value must be quartered. How perfect is it that 416 / 4 is a whole number :3

a = (3 x 104 - 2 x 104) x (3 x 255) / (3 x 104)

a = (312 - 208) * 765 / 312

a = 79560 / 312

a = 255

Since a is 255, the Pokemon is caught. No exceptions.

Generation 3 and 4 use this formula:

Let's do some mathz.

a = [(3 x 416 - 2 x 416) x 3 x 255 / (3 x 416)] x 1

a = [(1248 - 832) x 3 x 255 / (3 x 416)] x 1

a = [416 x 3 x 255 / 1248] x 1

a = [280800 /1248] x 1

a = 255 x 1

a = 255

Master Ball still catches.

Generation 5 follows the same formula as 3 and 4, but the bonusstatus is higher than Gen 3 and 4 for sleep and freeze. Even if you factored those in, the catch rate will be higher than 255, which warrants a catch.

Formula sources

Catch rate source for Master Ball

Mewtwo's catch rate