Yes.........the light from which they grow is the same source of energy as the heat. It just changes wavelength. Yes, any shadecloth will diminish light available for growing and that's why they are called shade cloths, so one chooses as high light transmission as they can and still control heat. Yes, it would be better than trying to grow under a tarp, unless the tarp is small enough it would perhaps just cover the area of roof when the sun is at its zenith and still allow rays in coming at an angle so they are less intense.

Thanks. That's kind of what I though, but wanted to know for sure. The tarp just covers a major part of the roof and south side. when the sun looses it's strength I will remove at least part of it.