It is possible that 'body-dragging' wasn't implemented in the Shadow of Chernobyl game engine and so (I assume) wouldn't be available in any mods based on that game. I am pretty sure I have seen other mods use [L-Shift]+ ['Use' key], but they might have been based on the later Call of Pripyat engine.
If anyone here has used dragging successfully in StalkerSoup, please let us know.