Nope. Private ctors have to be called from within the same module,
whether implicit or not:
test.d:
class Foo
{
    private this() { }  // Error: constructor main.Bar.this no match
for implicit super() call in constructor
}
import test;
class Bar : Foo
{
    this() { }
}
void main()
{
    auto bar = new Bar();
}