Depending on the depth and optical density of the clouds, cloudy nights would just mean that the target area was lit by a diffuse glow - as would, to a lesser degree, a wide area around it.
Practicalities aside, I'd be intrigued to know what effect regular sunlight at the planned intensity would have on local flora. Would photosynthesis still occur, albeit at a much reduced rate (bearing in mind that its quantum effects that are involved here, so a photon of the right energy should still do the trick even if there are way less than usual numbers of the things incoming)? Would it play hob with plants natural cycles?
I still think it's a bad idea, albeit not utterly unfeasible, anyway!