If I ask you to write a program that returns false if 4 is an odd number and true if it's an even number, you would say that's trivially computable:
def is_four_even(): return 4 % 2 == 0
Of course there's an even _simpler_ function:
def is_four_even(): return true
The two are both valid ways of computing that function. Four is even, it has always been even, you don't need to check if it's even, you can just return true.
For all these complicated questions about that people are all getting wrapped up about the only difference is that we currently don't know how to write the first version of the function, and we don't know which of "return true" or "return false" is the correct version of the second form of the function, but _the second form surely exists_, which means that it is computable. Either P=NP or P!=NP, and that has been true or not true since the beginning of time, and _one_ of those two functions would have been correct to use from the beginning of time. It's computable, we just don't know which one to use right now.
As soon as someone proves the status of P?=NP, you can just pick one of the two ('return false' or 'return true') if someone asks you write the function. It also doesn't really matter if a statement is provable in theory or not. Whether or not it's possible to prove that P?=NP, it is either true or it's false and it has always been either true or false, and one of those two programs is correct.