Generally one tries to minimize the fog level, because that's silver that could be used in the image, but if the film has enough density range, as most film does, you can just print through the base fog. It's more of a problem, though with alt processes, where elevated fog can seriously increase exposure times and you need all the density range the film can offer.
The only possible advantage might be if a little fog density pushes the shadows up the curve to improve shadow detail, sort of like flashing, but you would have to do some testing to see if that really works.
On prints no base fog is acceptable, so print developers usually include restrainers or anti-foggants to eliminate it.