The storm surge is way more likely to bring in a lot of oil than it being picked up by rain would.
That oil will stick to anything it comes in contact with. The water will recede somewhat clear, but what a mess being left behind.
You're right.
I didn't mean or suggest that all or even most of the oil would be airborne. I meant that some oil/toxic dispersant from this huge oil spill would be picked up by hurricane force wind. The hurricane would act like a huge centrifugal vacuum filter.
In industry, to separate solids from liquid in slurry, the heavier solid particles are deposited on the wall of a drum rotating at high speeds, creating the centrifugal force. The same principle could be at work in a hurricane swirling at high speed (the drum) and the wall is at the eye of the hurricane. The rotating wind velocity acts as a giant agitator kicking more oil/dispersant that creeps up the wall from the water surface due to reduced pressure at higher elevations (vacuum effect.)
The oil/dispersant droplets (solids) will be carried toward land and come down when the hurricane , hits land, wind velocity reduced thus weakening the centrifugal force and that results in dropping the heavy hydrocarbons on areas in the hurricane's path.
The only thing that could reduce or maybe eliminate this scenario is to immediately burn as much as possible of the oil spill while the Gulf is calm.