Absolutely run it. Have had bad experiences when I did not or had it off for even a short amount of time (you will see on here its about a 50/50 split on those who do and those who don't)
I would absolutely recommend running it. I had two 40 gallon tanks I ran them on, now I have an Elos 120 that I just got three weeks ago. I just added a 25w UV and I have noticed immediate water clarity.
I have a UV I'm hooking up to my new tank. My LR has some algae I'm hoping it will help plus I'll be adding some new fish at some point. But not sure if it's ok to run while feeding live foods? I'm guessing not. My goal is to have mandarins. It may affect their food supply. I do know the flow rate is important.
Run it ! Water clearity , less algea , no iche !!!!!! Plus I don't even use a skimmer anymore and haven't done a water change in 2 months !!! All you need is a big refug and a uv and let nature do it's course ! U won't believe the coral growth and health either , it's actually pretty insane