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