I may get someone (or two or three...) who doesn't agree with me here but here is what I believe from what I've seen with my wrasse (I've had flasher, fairy, and melanarus) and anthias, and from what I've read. The wrasse are more known to eat "pods", and even peck the pods from the rocks. The Melanarus, 6 line, 4 line, and yellow coris are known to do this. They are also decent at eating pests.
The anthias on the other hand are now known to do so... at least not from peckin off of the rocks like a mandarin does. They are known to eat from the water volume so whatever pods come there way through there I'm sure they will grab if they are hungry. But because they don't forge off of the rocks and glass I don't believe that they will compete with the mandarin. The pod population that the mandarin has been eating will most likely continue to be the same as it is today. Also... as you probably know, there are many types of pods (and I don't just means copepods and amphipods). More likely they wouldn't even eat the same types of pods.
You are right however in saying that they need to be fed multiple times a day, but so do the wrasse so if you weren't doing it for them... shame on you. Jk! Pretty much any active fish you will want to feed multiple times a day. I think I have my feeder set to go off 5 times a day and then I randomly add a blend of something or frozen mysis soaked in garlic. Being that they eat often they also poop often so you'll want to be aware of your parameters and possibly increase you water changes. It may be a little different caring for your anthias and wrasse but the one thing I personally wouldn't worry about is your mandarin's pod population.... and that is if you are certain you have a strong pod population with a mature tank.
Don't take all of this for 100% but this is just what I've observed and found through research. It will be great to hear others chime in!
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