Probably not. You might hear that all crabs are omnivores and can be nippy around corals, however this is pretty rare in emerald crabs, provided they have enough food. He probably enjoys hanging out there or cleaning the coral as your rock seems pretty new and might not have a ton for him to nibble on. You'll notice pretty quickly if your emerald is eating your coral- I've only had one start to munch some zoas out of probably 40 emerald crabs. They are not subtle about it
I have two in my tank and they will hang out around the coral as pictured but not harm them. It is very important to make sure they have a good food supply and they will not harm corals.
I watched mine just eat my frog spawn. Brand new crab and coral. Maybe it’s because I’m just starting my tank and there’s nothing else for him to eat yet? I am over a month in but my LPS sold him to me and now I wonder if I should be giving him back until I have a bubble algae outbreak or something more.