How big is it relative to the tank? Obviously every little bit helps, but if nutrient reduction is your goal I wonder if there aren't more efficient ways to use the space? Balls of chaeto provide other benefits too though, like a place for pods and other planktonic animals to breed, but you need enough flow to keep the ball relatively free of detritus and good lighting. The standard wisdom is that chaeto should 'tumble', but there are some writers on WWM that don't think it's critical, and I've grown it in the past in a little HOB fuge that didn't make it tumble. However, in that case the majority of your growth will be up at the top which I think might decrease it's effectiveness, though that really depends on the geometry of the chamber more than anything (is it a deep column, or wide and shallow, etc.)
Have you read through the wet web media pages on refugiums? There's a diversity of opinion there that covers pretty much every refugium case. Sometimes their advice is conflicting (don't use caulerpa! caulerpa is fine!), but if you have the patience to read through their pages of FAQs, you start to get a sense on what the consensus for the best way to set up a fuge is.
I'd say that if your goal is bang for your buck nutrient reduction in a limited space and you do want to do it with macro algae for all the other benefits that provides, your initial thoughts were probably right - a dedicated chaeto chamber is the best choice. I wouldn't put any sand or rock in there, as your'e not going to have enough space for something like a deep sand bed to do anything but create problems, and rock would just take up space that you want the chaeto to occupy. If you're concerned about flow, you might want to investigate whether or not a small powerhead could add the flow you're looking for in that chamber.
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