If the parents were indeed Narragansett Semi-Color Semi-Gray split to Black Winged Bronze, any Royal Palm poults produced will be pure Royal Palms. There is also the possibility of some pure Narragansetts being produced but they will look the same as the Narragansetts split to Black Winged...
One of the possible outcomes from that pairing is Royal Palm poults. When first hatched, Royal Palm poults are white and don't develop their black markings until later.
If both birds are pure and there are no hidden recessive genes, according to Porter's turkey color calculator the poults produced will be Narragansett Semi-Color Semi-Gray. Here is the link to a mature tom of that variety. I did not see any pics of what a hen will look like...