Most people don't, though it does take it out of the water, which is why you run it so it doesn't foul your water. But you could turn it off for a bit and it wouldn't hurt.
like said most people dont, but the problem with turning it off, you have the possibility of leaving it off maybe for a day or two...liquid suspension type foods tend to foul the water(actually most foods) and good filtration/skimming reduces the chances of the water going "bad"
i don't run a skimmer at all and I dose with Seachem's Reef Plus and DT's Phyto. I don't have any problem with my water quality . I think the key is to always start with less than the recommended dose and see how your tank reacts and work from there... nothing bad, increase it a bit