There are specifically designed turning departures and the obstacle clearance surface analysis reflects this. The minimum altitudes are a blank worst case scenario so as to not have to consider each aircraft turn performance for obstacle clearance.
That being said, RNP DEP are custom, and the obstacle clearance surfaces, coupled with turn degradation performance are considered. After you calculate the performance in a turn, then you must consider the bank limitation of each aircraft type.
Many aircraft are bank limited below 400 feet. I think the 747/777 are limited to 8 degrees below 1000 feet, and 3 degrees below 500 feet?