Only a pair of polarized sunglasses can help you see better in the heavy rain if you find it difficult to see the road while driving. But non-polarized sunglasses will make it darker and harder to see the road. polarized sunglasses can work well when driving in the rain during the daytime because they can help block horizontal components of scattered or reflected light. That is to say polarized sunglasses can counteract the scattering of light in the rain to help driver see better. But they are not suitable for driving at night.
I don't think it is good idea. Raining day usually have many cloud and in low visibility, you no longer need sunglasses because sunglasses are used in sunny day (strong sunshine) to increase visibility. If you wearing it in environment with low visibility, it will bring your nothing but darker and more dim vision. From this point, it will a very bad idea to wearing sunglasses when driving in heavy rain.