std::is_constructible on type with non-public destructor

What is the expected result for std::is_constructible on a type with a private or protected destructor?

For instance, I can still construct such an object on the heap even though only a friend can free it:

#include <type_traits>

class Foo
{
    friend void freeFoo(Foo*);
public:
    Foo()
    {}
private:
    // Destructor is private!
    ~Foo()
    {}
};

void freeFoo(Foo* f)
{
    delete f;  // deleting a foo is fine here because of friendship
}

int main()
{
    Foo* f = new Foo();
    // delete f;   // won't compile: ~Foo is private
    freeFoo(f);    // fine because of friendship


    if(!std::is_constructible<Foo>::value)
    {
        std::cout << "is_constructible failed" << std::endl;
    }
}

The final check for is_constructible will fail on both gcc and Visual C++ (gcc demo on coliru).

Is that the required behavior by the standard? If so, is there any way to check whether the type has a specific constructor, regardless of the access specifier on the destructor?