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Yes it will run on the drive side but the axle will spin the wrong direction so it will not work for what you are trying to do. That is why they are called "reverse" rotation. The teeth are cut in the opposite direction from normal so when the pinion spins from left to right on a regular set lets say the ring gear will move from top to bottom. In a reverse cut set the pinion will still spin left to right but the ring gear will now move from bottom to top.
You cannot put "reverse rotation" gears in a standard housing. Actually, reverse rotation is not an accurate term, nothing in a reverse rotation gearset spins backwards. It is called reverse because the spiral of the pinion is cut in the opposite direction from normal. It is to retain gear strength when the centerline of the pinion is above the center of the ring gear. A hi pinion axle is not a flipped over low pinion axle, it still has the pinion on the same side of the ring gear as a low pinion axle. It is just raised up.