It's perfectly fine, since a turkeys organs and the breast meat are separated and nothing is damaged when you shoot them in the head it's not nearly as important to get the meat out and cooled down as it is with other game.
I've taken a bird on a Sunday morning hunt and didn't have time to process so it waited in the truck while I went to church and showed it off to all the hunters after, then ran it to get weighted for a local big bird contest... Then took the breast meat out, it fried up delicious!!! No worries