The PDF format is more like a metafile graphics format, PCL, etc. If you feed these a bitmap capture there isn't much to be done with it in terms of space savings. At best they might try to apply PNG-like compression but I'm not sure any of them do.

If you can make Word "print" to PDF then yes, at least text will be saved as globs of text with font-and-layout markup. I'm not sure how they manage metafile graphics but it would have the chance to capture the vector-based elements of the drawing as vector graphics. That's how print drivers work.

But screen captures would be worse than what we've demonstrated already. Far worse in nearly every way.