You mean plugging it into a generator directly? It depends on the output wattage and if it's sufficient for the pump. As for other hurricane dangers, I'm not familiar with them, but I wouldn't leave a solar cover on the pool any more than I'd leave lawn furniture out.

Unless the pool empties I don't see what harm a correctly sized generator would do.

Still, if the storm is only a day or two it might just be better to shut down and batten down the hatches.