Welcome! I have a dragon eel in a mixed reef, and i can tell you depending on the eel it will certainly cause a significant amount of more maintenance. They produce ALOT of waste and make it difficult to keep low and stable nitrates and phosphates for sps. It can be done for sure, just be prepared for more water changes and heavier filtration. Not to mention a big eel like mine will break alot of thinner branching sps fairly often.
So if you dont have a certain eel in mind there are a few choices that i would recommend.
1. If you're experienced and can make sure it cant get out ribbon eels are beautiful additions. Since their bodies stay thin and light they wont break any coral, and they dont eat nearly as much as larger species, therefor less waste. And do to their size they also can only eat the smallest of tank mates. But they are also one of the most difficult eels to keep.
2. Gold dwarf moray, these guys are also one of the smallest species of true morays. Like the ribbon eel, smaller eel=smaller prey, less waste. Easier to care for than ribbons and with a thicker body is easier to keep from escaping.
3. Snowflake and zebra morays. These guys are both the least aggressive species and often are the most likely to get along with other tank mates. With the zebra being the most docile and most friendly. Both are very hardy species. These guy's diet mostly consists of shellfish and crustaceans so be careful if you want to add any. But they both grow fairly large. The snowflake can grow to 30-36in long with a pretty thick body. The zebra can grow even longer but often stays a little thinner than most morays that size. Both will still produce a ton of waste.
4. Other species can still be used but are more likely to grow bigger and be more aggressive.
Dont pair eels with any fish they could swallow, some individuals may be fine with smaller tank inhabitants but if you attempt it just be prepared for them to becone an expensive meal. MOST morays are fine with cleaners like wrasses and shrimp, but again it depends on the individual.
Lastly STAY AWAY from green and tessalata/honeycomb morays. The average hobbyist is not equipped to handle these species as they can easily top 6ft and need 1000+g minimum. You will be hard pressed to keep them with other fish and coral.