Nope. Even open diffs send the power to both wheels at all times -- again, as long as both wheels have traction. The only time you get the power going to one wheel is when that wheel is off the ground or slipping, because the power always takes the path of least resistance. However, that will happen whether it's the left or the right wheel that is slipping.
Limited-slip differentials prevent one wheel from spinning too much faster than the other, hence the term "limited slip." This makes sure that both wheels get at least some power, even in the worst conditions.
Lockers obviously lock both wheels together.
Gear-type torque biasing diffs naturally send more torque to the slower-spinning wheel, but with a catch: if one wheel is entirely off the ground, it behaves like an open diff and just spins the wheel with no traction.