I understand your concern about falsy values, but this does not fix this (unlikely) scenario. In case MyNamespace is 0 (or any other primitive value) your code would fail on this line:

MyNamespace.MyClass.prototype.sayHello = function () { return this.string; }

Since MyClass reference will be discarded right after the number is coerced to an object. Another example below:

var n = 0;
n.MyClass = function(){}
n.MyClass.prototype.sayHello = function(){} //TypeError: Cannot read property 'prototype' of undefined