How can I check if a move constructor is being generated implicitly?

Declare the special member functions you want to exist in MyStruct, but don't default the ones you want to check. Suppose you care about the move functions and also want to make sure that the move constructor is noexcept:

struct MyStruct {
    MyStruct() = default;
    MyStruct(const MyStruct&) = default;
    MyStruct(MyStruct&&) noexcept; // no = default; here
    MyStruct& operator=(const MyStruct&) = default;
    MyStruct& operator=(MyStruct&&); // or here
};

Then explicitly default them, outside the class definition:

inline MyStruct::MyStruct(MyStruct&&) noexcept = default;
inline MyStruct& MyStruct::operator=(MyStruct&&) = default;

This triggers a compile-time error if the defaulted function would be implicitly defined as deleted.

As Yakk pointed out, it's often not relevant if it's compiler generated or not.

You can check if a type is trivial or nothrow move constructable

template< class T >
struct is_trivially_move_constructible;

template< class T >
struct is_nothrow_move_constructible;

http://en.cppreference.com/w/cpp/types/is_move_constructible

Limitation; it also permits trivial/nothrow copy construction.