If it's eating, odds are that it will be fine. Make sure that it's alert, that its stomach isn't sunken in, and that it's mouth looks ok.
A reef is pretty much the only tank that an idol has a chance of surviving in. If you throw it into a FOWLR, it won't do as well. It might pick at some lps here and there but I don't think it's known to do any real damage.
A cavaet is sometimes ones that are eating will just stop eating for no reason (or after it's shipped). Regal angels do this too. Finicky eaters turn down food for no reason at all.
It is NOT (repeat NOT) hard to get Moorish Idols to eat just about anything. The tough part is fulfilling their long term nutritional/husbandry needs which are mostly unknown/misunderstood at this point.
Spread the word: Just because you see a MI eating does not mean it is "in the clear". It will still be a very difficult task to get it to live longer than about 2 years.