Yes. Just for example, you can use a public function from the base class that manipulates private data, even in an instance of the derived class:
class Base {
int x;
public:
Base() : x(0) {}
void inc() { ++x; }
void show() { std::cout << x << "\n"; }
};
class Derived : public Base {
};
int main() {
Derived d;
d.show();
d.inc();
d.show();
}
With a properly functioning compiler, this must display:
0
1
...showing that the data in the Base object is present in the Derived object, even though it's not (directly) accessible.
Of course with almost anything in C++, there's the "as-if" rule -- if the compiler can determine that it can somehow produce the correct observable behavior for the program, even without including the private part(s) of the base class, then it's free to do so. The most obvious example of this would be if you included something (member function or data) in the base class that was simply never used in practice.