it depends on the state/county/city you are in. Federal law only recognizes dogs as service animals. Only a few places have laws that offer greater protection than that in regard to what is allowed. Once you leave that area, you no longer have those rights. So, even if a service rooster is allowed where you live, it might not be allowed if you go on vacation.
ETA: just wanted to also say that there is no law or requirement that a service animal be certified.