Does a company's success at employee retention predict their recruitment success?

Of course, at least as the correct steps taken at the recruitment stage. Employees may leave the organization later due to team problems, role clarity problems, supervisor-related issues, etc, but high retention levels certainly indicate that the recruitment was successful.

We must also remember that90% or more of attrition happens due to supervisor related problems. Therefore, when attrition is low, I would tend to give the credit to the line managers who manage them on day-to-day basis.

Hope this clarifies.

Of course. Right candidate will be right position, this responsibility is for Human Resources Department. However, it is not limited by recruitment. HR will take initiative to increase the retention through long term  career path.