Parrots might be too quick to get the food, leaving little for the polys. Other than that, if you have sufficient hiding space for the polys, I think it'd be alright.
Because parrots are usually pigs, it will be hard at feeding time. But anything is possible. If you have to divide a small section of the tank for your bichirs and put the parrots in the other section.
parrots are definitely pigs.they are always hungry too. it is hard to get food down to my featherfin and pictus catfish that are with my parrots. i try to distract them with floating food then drop in sinking food for the cats. they still go for the sinking food but, the cats get some of it.