Not exactly... Power is equally divided between the two wheels. If one happens to have less tractive effort than the other, then all power can be directed to that one with the less traction.
Also, when turning corners, the outside wheel must travel farther due to it's larger arched path. So in this situation the differential will split the difference and allow the wheels to turn at slightly different speeds but still provide power to each.
With both wheels in the air, and turning the drive shaft, it's possible to have only one wheel turning. If there is more drag from the brakes or bearings on one wheel, the differential can reroute all rotation to the other wheel. If you hold the wheel that turns, the other wheel should then turn.
As Don mentioned, if you were to hold the drive shaft and rotate one wheel, you'll find that the other wheel will rotate in the opposite direction. This is due to the arrangement of the gears within the differential. This is all normal.
Merle