HEy Mark,
No, I've never used egg yolk as a binder, but I bet it would work. I remember seeing friends' houses that got egged when I was in high school....and once that stuff dried, you may as well just give up trying to get it off.
The only problem I see is the fact that arrows are usually sanded very smooth, and that could cause the paint to peel or chip off after being shot. Remember, paint doesn't like a smooth surface, so regardless of what you use for a binder, rough up the surface where the paint will be with 150 grit sandpaper....this will give the paint something to grab onto and will make a much more durable finish.
Post some pics when you're done..I'd love to see how it turns out!