I have always run my skimmer during cycling. In fact you do water changes as well. I would not run carbon during the cycle or waste time with lights, but flow-skim-temp-salinity should be the focus. Nothing living (other than the rock) should be in the tank. The skimmer removes organic compounds from the water but the skimmer helps to get rid of excess proteins. You will loose a little of the good growing bacteria, but not enough to be a problem. If you look up "curing live rock" you will even see skimmers hooked up to the large vats where people are curing the LR they have prior to putting it in the tank. Like I said, the only waste would be to leave the lights on. Make sure that you have removed the sponges and other matter that has died in shipment and it will improve the cycle/cure. Hope that helps.
LOL, I always leave a light on my curing rock . Usually the stuff I get from Ken has plant life that I try to preserve as well as other potential light needing critters. It will encourage algae though (one of the reasons I cure outside my tanks for two weeks first).