Can a move constructor be implicit?

The compiler synthesizes a move constructor if it can and if there is no user-defined copy constructor. The restriction that no move constructor is synthesized if there is copy constructor is intended to avoid breaking existing code. Of course, all members need to be movable. The exact rules are a bit more involved.

Yes, from the C++11 draft, 12.8:

If the definition of a class X does not explicitly declare a move constructor, one will be implicitly declared as defaulted if and only if

• X does not have a user-declared copy constructor,
• X does not have a user-declared copy assignment operator,
• X does not have a user-declared move assignment operator,
• X does not have a user-declared destructor, and
• the move constructor would not be implicitly defined as deleted.

The last condition is specified with more detail later:

An implicitly-declared copy/move constructor is an inline public member of its class. A defaulted copy/move constructor for a class X is defined as deleted (8.4.3) if X has:

• a variant member with a non-trivial corresponding constructor and X is a union-like class,
• a non-static data member of class type M (or array thereof) that cannot be copied/moved because overload resolution (13.3), as applied to M’s corresponding constructor, results in an ambiguity or a function that is deleted or inaccessible from the defaulted constructor,
• a direct or virtual base class B that cannot be copied/moved because overload resolution (13.3), as applied to B’s corresponding constructor, results in an ambiguity or a function that is deleted or inaccessible from the defaulted constructor,
• any direct or virtual base class or non-static data member of a type with a destructor that is deleted or inaccessible from the defaulted constructor,
• for the copy constructor, a non-static data member of rvalue reference type, or
• for the move constructor, a non-static data member or direct or virtual base class with a type that does not have a move constructor and is not trivially copyable.

Plainly speaking, the move constructor will be implicitly declared if:

1. The class does not have user-declared any of the other special member functions.
2. The move constructor can be sensibly implemented by moving all its members and bases.

Your class obviously complies with these conditions.