Yes, I think there should be a way to do it in Corona - either with the same object settings or through RaySwtch or shadowcatcher.
I generally don't see anything being done in the video which is not possible with Corona.
If you have a specific scene/case (screenshot or video will help) with exact thing to accomplish, I may help you further and more precisely.
If it is fine for you, you can share a scene so I can "fix" it directly in it.