100% it would have. One of the main things the LiDAR system does is establish a "ground plane", which is the surface on which the car is expected to drive. Any hole or protrusions in that plane stick out like a sore thumb to a LiDAR system, you'll be able to see it in the raw data without much of a feature detector, so detecting them and reacting is fast and reliable.
Contrast with Tesla's "vision-only" system, which uses binocular disparity along with AI to detect obstacles, including the ground plane. It doesn't have as good a range, so with a low- profile object like this it probably didn't even see it before it was too late. Which seems to me a theme for Tesla autonomy.
In addition to detecting the object, Waymo has to make some determination about the material. Rigid heavy metal = slam on the brakes and/or swerve. Piece of tire or plastic bag = OK to run over if swerving or hitting the brakes would be more dangerous. Really hard problem that they're concerned about getting right before they open up highway driving.
LiDAR is also good for that because you can measure light remission and figure out how much of the LiDAR energy the material absorbed. Different materials have different remission properties which can be used to discriminate. Which is a compounding advantage because we tend to paint road line markers with highly reflective paints. This makes line markers blindly obvious to a LIDAR.
Stereo vision might have helped too to assess the size of it, but from the pre-crash display at 0:07 it looks like the Tesla didn't see the object at all, which is a bit surprising since it was large enough, and very clearly looked like exactly what it was - a big chunk of metal.
The car reacted the opposite a human would. If you saw something unidentifed ("road kill?") in the distance then you'd be focusing on it and prepared to react according to what it was. With an empty lane beside you I think most drivers would be steering around it just based on size, even before they realized exactly what it was (when emergency braking might be called for).
