That is correct, and the bonus is that you don't even need the CPL, just the CPL exams (as least it is for helicopters - check that for fixed wing). But it may be just as easy in the mddle of all those check rides just to do it.
There is no credit for your licence - you still have to take 13 exams. But it is only 250 hours of study overall.
Actually, there is always room for a dedicated instructor. Far too many of them have one eye on the student and the other on the clock.