Many of the attrations at SW are inside, so the hardest part if getting from attraction to attraction. If you're lucky enough to get scattered showers that day, you may even be able to get on the roller coasters.
It will depend on how bad the storms are that are coming in. Dizzy to sporadic rain will be OK. Heavy rains - the outdoor shows will probably not run as well the coasters and if the kids are young the Shamu play area would not be recommended.