Is a significant amount of light energy blocked by one planet such that there is noticeable cooling of the atmosphere of another?
It is detectable, but not substantial.
When Venus transited in 2012, it blocked about 0.1% of the light from the sun, which was unnoticeable. This is about 10% of the variation in the sun's brightness over it 11 year cycle. It is much less than atmospheric effects, such as variation in global cloud cover.
The biggest transit would be a transit by Jupiter, viewed from Saturn:
Even this would not cause notable cooling, and would not even be noticeable to someone who was not looking at the sun (our eyes adapt to variations in overall brightness)
Of course a transit by the moon, viewed from Earth, does cause noticeable local cooling.