But yes, there are advantages to paper, like the ability to easily draw diagrams and link ideas with arrows, etc.
On the other hand, if you need that, you could always use something like a Wacom tablet, or maybe some other touch-screen device with a stylus. That would give you the best of both worlds.
Are there tools that will let the user search "hand drawn" digital image ? One can always use tag like system, which one can't with paper, but then it is extra work, and adding "text" tags is easier when using something like org-mode, or just plain text.
Still, there are ways to make drawing somewhat searchable too.
The (typed) names of the drawings you make are searchable, as are the tags (if you've used any, and you should), and their location on your filesystem. If there's some writing on the same page as the drawing, that's potentially OCR'able, and then searchable. Finally, you could always combine drawings with typed text, wich will be searchable.