I think you’re out of luck for getting this extrusion to automagically become a separate object.  I can’t think of a way to do that.  I think your best bet is to use the Extract command to make a separate object out of selected faces. 

So this becomes a question of how best to select the faces in the extrusion.  I would try to select one of the big faces in the extrusion, then shift+double-click the big face next to it.  This should select the whole ring of extruded faces.

You can use the > key to grow the selection if you want to also select those smaller rings of faces near the body. 

If you run Mesh -> Extract now, your model will be split into three poly objects—the unselected part of the extruded shoulder pad, the selected faces, and the rest of the body.

You can select the two parts of the shoulder pad and use Mesh->Combine to make them back into a single polygon piece.

It’s not elegant, but I think this is the quickest way to get where you want to be.  Otherwise you might be stuck doing a lot of manual face-by-face selection and hoping you don’t miss one or include an extra one accidentally.