It wouldn't surprise me. There have been studies showing that removing speed limit signs actually improve safety as well, because people tend to drive at a safe speed. When weather is bad, people tend to still try to drive the speed limit. When weather is good, it actually increases the variation in speeds. And it's less speed that kills, it's variations in speed.
That being said, I don't know if the effects would stack - it might be better to have no speed limit AND the white line, or no white line with a speed limit, but having neither or both is less safe. Or it might be situational.
I just hope that self driving cars renders it all moot, though the mental processing involved is interesting.