In the absence of a PRIMARY
key, InnoDB/XtraDB will first try to use a UNIQUE
index. If neither exist it will make up an internal primary key that is not reliable between galera nodes.
You are correct that a PRIMARY
key is basically a UNIQUE
index with the only difference being that there can only be one PRIMARY
key. It is also used for the physical layout of the data but that isn't as important here.
As long as there is only one UNIQUE
index, you should be fine. However, I don't think it would be reliable if you add another UNIQUE
index. Because of that and for good practice, you should probably make that UNIQUE
index the PRIMARY
key.