>>282104305 (OP)
Yes.
It's probable that he wouldn't consider the supernatural explanation, but he would be able to narrow it down like L had to being a Japanese high school student in the Tokyo area with a family member in law enforcement.
From there, it would be a 400 chapter long arc wherein the Kira case comes up in about 5% of those chapters, and there'd be a moment in the climax like this
>Light scribbles down "Conan Edogawa" in the Death Note
>"WHY WON'T IT WORK RYUUK?!"
>Conan kicks a cement brick at his head, safely knocking him unconscious