Some would, yes! Notably: Tursa and Rathm would have the most complete souls. And, depending on if the Murk have, er..."devoured" anyone recently, they would too.

Wendel, Gahar, Grimlings, Thelesh, Uskal, and Wendel would register as having incomplete, or "fragmented" souls, as though they were once living but were improperly rendered. If a Murk hasn't absorbed anyone recently, they would too.

Nighthooks do not have bodies, and thus do not bear souls.

Neither Oolicks nor Mr. Skittles register as having souls at all.