It really depends on the skimmer.
In my case I have a ASM g-2 that's a recirc mod.So,none of the water from the sump gets run through the skimmer.Only the water from the tank overflow.
So I could put chaeto in the sump but not mud.I have my DSB and chaeto,rocks all in a 20L run via a split from the overflow.This water exits the refugium ito the sump and is pumped back to the DT unfiltered.
Personally,I wouldn't try to stuff too much into a refugium/sump.You'll be just asking for problems doing that.