The most obvious transferable skill is going to be understanding basic electronics. You might pick up the basics of how the internals of processors work. You will learn how to debug (both hardware and software) which is invaluable in almost any situation (not just computer engineering.)
When I was in high school, I built TI-85 PC-adapters. This lead me to an electronics class where I built a Sumo-robot, among other cool little projects. My direction was pretty much set from there. I went to college for Electrical Engineering and focused on RF design. However, I had a knack for programming so I always enjoyed microcontroller projects. (I spent 3 months as a design engineering intern and then took a career in sales.)
These days I can built prototype circuits, design my own PC boards, have learned enough ME to design enclosures, write Assembly code, program micros in C, and do PC-side applications in Cocoa or C#. (This of course doesn't even get creating SQL databases and writing un-readable PHP and Perl code.)
Part of why I tell the story is because the path you choose doesn't really matter. The Arduino is an excellent starting point if you have any interest in anything related to electronics.