Yes, gold filled wire can be drawn down. That’s how it’s made. It starts as gold filled rod and gets drawn into wire. Just make sure your drawplate is well polished, since you likely wouldn’t be able to remove any scratches without wearing through the plate layer.
Gold fill, also called rolled gold, and Sheffield plate are both built on the principle that the malleability of the base layer and that of the top layer are similar. When the billet is drawn or rolled the constituent metals decrease in thickness proportionately.