No they dont. Although the muppets in my local Reno dealer thought it did...
Think the ESP works by reducing power/applying brake to the spinning wheel.
The ABS is designed to cope with loss of traction under acceleration. It reduces engine power if either front wheel is spinning. So your acceleration is limited by the amount of grip the wheel with the least amount of grip has. An LSD in the same circumstance would transfer the power to the wheel that has grip.
The ESP is designed to cope with possible loss of control. It applies the brakes, I think only on the rear but I'm not certain, and may also reduce engine power.
Interestingly GM Holden produced an off-road capable 4WD that doesn't have any form of limited slip diffs. It uses the ESP. If, say the front left wheel is spinning it doesn't reduce engine power, it just applies the brake enough on the wheel that's spinning to transfer the power being wasted to the wheel on the other side that has traction. If both wheels on the same axle are spinning it applies the brakes on both so the power is transferred through the central diff to the other axle. Its a simple obvious idea that's only disadvantage is that it must wear out the brakes quicker. You wonder why other manufacturers don't do it. If one wheel is spinning apply the brake on that side. And only if both are spinning do you reduce the power. No hardware required to get the equivalent of a limited slip diff, just software changes in the ABS/ESP computer.