Hell, I don't even have a crazy-nice kit and I haven't had any problems. I know my voltage doesn't drop below 13; most HIDs should be fine even on 12, considering that's where they're often being powered when the headlights come on before start-up.
Just like hispls said; considering the normal power fluctuations between the key turning, start-up, idle, and high rev, even on an 'unloaded' electrical system, the drop in voltage in our vehicles shouldn't be anything dangerous to your lights unless you've got some serious drop, to the point where it could damage any electrical component in your car.