As is you won't have access to those functions. When you define a named JS function it's the same as if you were to say
var handleSuccessOfAPI = function(){};
In which case it would be pretty clear to see that the var is only in the scope within the block and there is no external reference to it from the wrapping controller.
Any function which could be called discretely (and therefore tested) will be available on the $scope of the controller.