Live copepods may well be a great food for many corals in your tank, though they're just "empty shells" unless they're artificially enriched with a diverse mixture of phytoplankton and amino acid/fatty acid supplementation.
The issue that you may find is that it's difficult and inconvenient to grow large amounts of any copepod. I've 4 different species under culture for several years, and the culture density is nowhere near what you can achieve with, for example, rotifers.
And for your average aquarist, buying a bottle or two of phytofeast and oysterfeast every once in a while is far cheaper and less work.