No. Sound is a sequence of pressure waves that propagate through a compressible medium, such as air or water. Sound has to move molecules in order to travel. Sound is transmitted from a source to the surrounding molecules, which vibrate or collide and pass the sound energy along until it eventually reaches our ears. The closer the molecules are to each other, the farther the sound can travel. This is why sound travels farther through water than it does through air and why it is impossible for sound to move through space.
Fog is made of tiny droplets of water. Sound waves interact with small droplets in such a way that sound undergoes attenuation and dispersion. Analogously, think of how clouds visibly appear white, even though they are made of water that is clear. It is because they are made of tiny water droplets, as is fog, and this affects how light, and sound, move through the medium.
Attenuation by sound waves in fog is a function of the frequency, or pitch, of the waves. This is why fog horns have a very low pitch, because their sound will travel farther than a screeching sound.
A recent sports blog argued that the Seattle Seahawks should hope for a home playoff game, as fog is common in Seattle. The idea was that with fog, the screeching cheers of the fans would travel a greater distance in a fogged-in stadium. However, if they get to play the Packers, they would do better to hope for non-union NFL referees.