If you have define a empty argument constructor to a Class, then user defined empty argument constructor will replace default constructor which generated by compiler.
The default constructor is the no-argument constructor automatically generated unless you define another constructor with no argument. Check JLS 8.8.9 for more details
is a user defined empty constructor called a default constructor?
No, It's called used defined constructor.
Or should there be no constructor defined in the class when we can speak of a default constructor when initializing an object?
Default constructor mean, Compiler generated, no argument constructor. Every other Constructors are called used defined constructors.