I really don't think it matters if they are alive or not. Of course I never let my cast just sit once casted, I'm always retrieving. Maybe having the minnow alive on a still cast will benefit you more.

I hook them two ways, thru the eye sockets or thru the belly and out the back. The last method keeps them on the hook longer and good for fast retrieves. It kills the minnow faster but I still catch tons of fish either way.