Unlikely. Near IR cameras (like what you have) work off of reflected energy, just like a regular camera. It's just a wavelength our eyes can't see. Far IR cameras (thermal) work on emitted energy (heat produced by an object). If you pump up the near-IR light source, it's just going to reflect off of the fog like your headlights do. (Though the IR might make it a bit farther through the fog than headlights, it still won't penetrate much further)
Good explanation of the different IR regions:
http://en.wikipedia.org/wiki/Infrared