Yes.
You can absolutely put two birds of different breeds or colors together, and show the resulting bird as whatever it is closest to - you're not likely to do well in the first generation (unless you're just changing colors), but its not uncommon at all to see very good show birds who have...
The terms "mutt" and "purebred" have no meaning in poultry.
If it meets the breed specification, it is the breed. If it lays olive eggs, it doesn't meet the breed specification. The ameracauna and aracauna specifications also allow for the bird only producing 50% of offspring that meet the...