Increasing muscular endurance only makes you somewhat stronger. Increasing strength on the other hand also increases endurance. So no the correlation does not go both ways.
The reason for this is:
Henneman's size principle
Muscle fibers are grouped together in motor units. There are typically 3 to 15 muscle fibers in each motor unit.
All motor units in a muscle receives the same electrical signal from the brain. The smaller motor unit only requires a weak electrical signal to engage. They contain only type I fibers: slow enduring. The larger motor units requires a stronger electrical signal to engage. They contain mostly only type II fibers: fast and strong but not enduring. When a motor unit engage all muscle fibers in that motor unit contract. The brain starts by sending a weak electrical signal first. This recruits only the smallest motor units and therefore only a small force is generated. It then increases the strength of the electrical signal gradually (but very fast) and more and more motor units are recruited and more and more force is generated. It does this until the produced force matches the requirements. This wonderful mechanism enables the same muscles that can be used to lift heavy weights to eg. perform brain surgery. As mentioned the motor units are recruited from the smallest to the largest based on the force demands placed on the muscle. This is Henneman's size principle. It has been verified in experiments using EMG measurements of muscle activity. It is therefore a scientific fact and not a postulate.
The size principle has one very important practical consequence: in order to recruit all motor units and train the whole muscle a high resistance must be used. A low resistance (such as 20 RM) do not recruit all motor units and therefore do not train the whole muscle.
Therefore the answer to this question is no, the correlation does not go both ways. Training with heavy weights trains the whole muscle. That includes the enduring type I muscle fibers and the stronger but not enduring type II muscle fibers. Training with heavy weights therefore makes you both strong, fast and enduring. Training with light weights on the other hand only train the enduring type I muscle. It therefore makes you enduring and somewhat strong.
For more practical advice regarding rep ranges I would refer to this article by world record holding powerlifter Greg Nuckols: https://www.strongerbyscience.com/powerlifters-should-train-more-like-bodybuilders/ He seem to advocate that powerlifters should train more like bodybuilders, that is in the rep range 8-12 in order to maximise hypertrophy, and as competition approaches they should switch to lower rep range to be neurologically prepared for 1RM.