Yes, you can run a generator during a storm, but only with proper protection. If you are asking, “can you run a generator in the rain,” an unprotected portable generator should never run in direct rain because water can cause electric shock, short circuits, and equipment damage.
Use a weather-rated cover made for running generators, not a tarp or enclosed shelter. Keep the generator outdoors, dry, stable, and away from doors, windows, and vents to reduce the risk of carbon monoxide.