I keep my not so reef safe fish and inverts in my refugium. I have filter socks first in my sump, so if any food chunks make it to my sump, it won't get to my refugium. I feed, but it's a very small amount.
My old sump didn't have filter socks and I was a terrible over feeder. I did not feed the sump because I saw food there.
I think it depends in the setup, and if you love feeding things like me. All living things need food, just as long as it is provided in some way you are golden.