I believe you are going to get conflicting answers here including from me but to be honest you may be mixing up your terms. A refugium is a refuge. A place for micro fauna and small animals to live without fear of being eaten. Pods, small bits of macro algae, corals, and what not. In theory they make their way from there to the display and then they become food source provided it is designed for migration between the two. If that makes sense. In this sense of the term and use you will not get pristine or higher clarity of water.
On the other hand you could use the same HOB container and put in some macro algae that with proper lighting can grow and export nutrients. It will also allow some area for pods and mini starts potentially. Since its primary role is nutrient export a high quality macro algae should be used. Again since we are talking about 20 gallons I'm not sure this is going to add clarity to your display.
In either case not sure this is going to do what you want. Macro algae removes nutrients when properly grown and harvested. Export of nutrients does yield water quality so maybe I'm tripping up on the pristine part.