Idk if the Blood Parrot is considered a cross between 2 different kinds of cichlids with different breeding styles...they were all SA/CA cichlids which usually lay eggs.
You usually find mouthbrooders in Africans and egglayers in SA/CA cichlids. So your odds of this happening are very slim. (At least in the wild). The only real way i could see this happening is in a lab. But we really don't need another hybrid thread here so...
So my answer to your question would be: yes, but only with the help of humans.