They will be fine with the moonlights on. The only reason lights are shut off to begin with is for less risk of shock such as from weak lighting to very strong lighting.
I keep my lights on even and i have never had a problem. Usually coral is open first few hours with lights on, i may feeding it depending what it is and then its lights off and moonlights on. No harm at all.
29g Mixed Reef, 150w 14k Phoenix MH w/ Moonlights, Reef Octopus BH1000 HOB Skimmer, Ecotech Vortech MP10es, ReefKeeper Lite (Plus), PH Probe, Temp Probe, ATO, Carbon/GFO Reactor.