I understand "light up, sights up," and certainly agree especially with a 6 o'clock hold and iron sights. But I don't know if that's a factor using center hold and a scope?
Yes, the light will affect how you perceive the target through a scope. As for the rain I have shot in the Midwest Regional VHA matches at the Wabash Conservation Club in all kinds of weather and at 400 yards in the rain there was only minimal difference in the poi but the ambient light was even, whereas a light change from cloudy to sunny could move you 1 moa or more especially if there is mirage involved.
Most people would not notice a 1/2 minute or so change in the elevation of their shots unless they are trying to keep them in the X-Ring. The change is the same whether it is a post, aperature, or a scope.
As far as bullets "hydro-planing" on rain drops....no. The supersonic shock wave ensures that a supesonic bullet never touches the rain drops. The shock wave pushes the rain drops aside.