Update: The proposed resolution of CWG 1734, currently in "ready" status, would modify [class]/p6 to read:
A trivially copyable class is a class:
- where each copy constructor, move constructor, copy assignment operator, and move assignment operator (12.8 [class.copy], 13.5.3
  [over.ass]) is either deleted or trivial,
 
- that has at least one non-deleted copy constructor, move constructor, copy assignment operator, or move assignment operator,
  and
 
- that has a trivial, non-deleted destructor (12.4 [class.dtor]).
 
This renders classes like
struct B {
    B() = default;
    B(const B&) = delete;
    B& operator=(const B&) = delete;
};
no longer trivially copyable. (Classes of this sort include synchronization primitives like std::atomic<T> and std::mutex.)
However, the A in the OP has a implicitly declared, non-deleted copy assignment operator that is trivial, so it remains trivially copyable.
The original answer for the pre-CWG1734 situation is preserved below for reference.
Yes, somewhat counterintuitively, it is trivially copyable. [class]/p6:
A trivially copyable class is a class that:
- has no non-trivial copy constructors (12.8),
 
- has no non-trivial move constructors (12.8),
 
- has no non-trivial copy assignment operators (13.5.3, 12.8),
 
- has no non-trivial move assignment operators (13.5.3, 12.8), and
 
- has a trivial destructor (12.4).
 
[class.copy]/p12:
A copy/move constructor for class X is trivial if it is not
  user-provided, its parameter-type-list is equivalent to the
  parameter-type-list of an implicit declaration, and if
- class X has no virtual functions (10.3) and no virtual base classes (10.1), and
 
- class X has no non-static data members of volatile-qualified type, and
 
- the constructor selected to copy/move each direct base class subobject is trivial, and
 
- for each non-static data member of X that is of class type (or array thereof), the constructor selected to copy/move that member is
  trivial;
 
Similarly ([class.copy]/p25):
A copy/move assignment operator for class X is trivial if it is not
  user-provided, its parameter-type-list is equivalent to the
  parameter-type-list of an implicit declaration, and if
- class X has no virtual functions (10.3) and no virtual base classes (10.1), and
 
- class X has no non-static data members of volatile-qualified type, and
 
- the assignment operator selected to copy/move each direct base class subobject is trivial, and
 
- for each non-static data member of X that is of class type (or array thereof), the assignment operator selected to copy/move that member is
  trivial;
 
[class.dtor]/p5:
A destructor is trivial if it is not user-provided and if:
- the destructor is not 
virtual, 
- all of the direct base classes of its class have trivial destructors, and
 
- for all of the non-static data members of its class that are of class type (or array thereof), each such class has a trivial
  destructor.
 
[dcl.fct.def.default]/p5:
A function is user-provided if it is user-declared and not explicitly
  defaulted or deleted on its first declaration.
Indeed, this has been a source of problems for the committee itself, because under the current definition atomic<T> (along with mutexes and condition variables) would be trivially copyable. (And obviously, allowing someone to memcpy over an atomic or a mutex without invoking UB would be ... let's just say seriously problematic.) See also N4460.