the "dry" amp head or preamp in the wdw rig feeds the effects via line out signal derived from a load box of some kind if it's a head, or preamp send, or slave ou if the amp has itt, and then split out to the effects.
the dry line level signal never needs to be inserted into the mixer, that is what the dry amp/cab is for. it just has to feed the effects inputs. in the case of a preamp you have to run a separate power amp for that dry signal as well as the stereo power amp for fx. matrix makes a nice compact 3 channel power amp for just that need.