Reflectors actually do diminish lumen output. Some far more than others, there was s good forum that tested the different hoods and their efficiency. But basically when the hood reflects light it loses light there in three ways: one the surface itself isn't 100% reflective, so some is absorbed. two not all the light is reflected in the right way, some of the light gets reflected back into the bulb which means passing through it again and two layers of glass. Three reflected light travels further to get to the plant, so applying the inverse square principal you lose light. If the hood is air cooled you lose about 10% from the glass, but you make up by closing the distance to the plants.
So with a hood on a horizontal setup you gain tons of usable light and effectively increase the lumens your plants get by a very large percent, I would sat 40% at least. But you do lose lumens technically. The only way to not lose lumens is to grow vertically, but then keep in mind each plant is getting less light(though generally more usable) due to it not being focused.