If and when your wheel bearings fail or wear out, it can't directly damage the transmission. However, it can indirectly cause transmission problems down the line. For instance, a bad wheel bearing can cause excessive vibrations to reverberate throughout nearby components. This would inevitably lead to the transmission, putting added strain on it. On top of that, a bad wheel bearing would allow the rotation of the wheels to have more resistance. Once again, this would put more stress on the transmission, especially if your car is front-wheel driven. Thus, it's crucial that you have bad wheel bearings replaced ASAP.