You could do that, or as Cooper mentioned you could use silicone tubing and connect the output to your manifold (ideally you would replace the 1/2in barb with 3/4 in, but it’s not the end of the world if you don’t).
Pulling water from the display and pumping it straight back in is going to be the most effective way to treat algae/parasites, but I think most people would agree that it’s not necessary unless you have a severe parasite infestation. You’ll still see results going from sump to display or sump to sump, but making it a closed loop in the display allows it to be a bit more effective.
This is a good video that might help you out