I have a few minor suggestions. I believe it will work great as designed but...
1 - I would split the line coming from the tank to create the input to the fuge. That way all of the water going into the fuge comes directly from the tank. The problem with your setup is that the refugium critters will not get any detritus from the tank. The way you have it some of the water leaving the fuge is just pumped back into the fuge. And, the circulation in the display tank is reduced directly by the water diverted to the refuge.
Add a ball valve after the split to the refugium on the leg going to the skimmer. All of the water will want to fall straight down. The valve will allow you to force some of the water all the way over to the refugium.
2 - I would put the input to the fuge against the glass in the corner closest to the overflow out of the fuge and put an elbow and the bottom of it. I would have the elbow placed almost at sand level and pointing along the glass on the long side. This will create a circular current and allow the sandbed infauna to capture detritus coming from the tank and remove it for you.
3 - I would have 1/2" - 1" of live sand at the bottom of the Refugium.
Guy