March-April 1942? Is this supposed to be an IJN analogue to the Doolittle Raid?
The fog of San Francisco is famous, but it's not a year-round occurrence. I live in the Bay Area and March-April is absolutely clear and beautiful in San Francisco. Also, fog doesn't really penetrate past the SF peninsula, so once those ships break into the East Bay, all bets are off.
However, assuming you want to just handwave getting the ships to the bay, to answer your questions...the ships would never make it out of the bay afloat. Any damage inflicted would be quickly repaired and the military gains would be insignificant. Still, the raid would have a devastating impact on the American public. It would be yet another demonstration of Japanese might and American impotence. Heads would roll. If it happened in late March, they might even catch the Hornet at Alameda, prepping for the Doolittle Raid. That would kill the Doolittle Raid, which might butterfly away Midway. This would definitely prolong the war, but not change the outcome. Post-war, no change.
This actually turned into a pretty fun thought exercise, but its utterly unrealistic because the scenario is too ASB.