No, this DUI you were convicted of in San Francisco, California a little over 7 years ago would not be off of your CA driving record yet.
As of January 1, 2007, new California legislation extended the reporting period for DUI offenses from 7 to 10 years for all public requestors, including insurance companies.
The CA Department of Motor Vehicles states that even if a DUI was previously taken off of your record (due to the previous time period of 7 years) that it will now appear back on your driving record and will remain there until 10 years from the violation date. So for instance if you received a DUI in June 2000 and it was previously taken off your record after 7 years it will now show back up on your driving record and remain there until June 2010.
Under this new California law, you may not qualify for a good driver discount again until 10 years from the date of your DUI violation. Up until 2007 a DUI may have been considered by an insurance company for premium surcharges for a period of seven years however now it can be considered in CA for ten years.
So if your DUI was less than 10 years ago it will still be on your driving record for public requestors to see and thus if you are asked on a license application if you have a DUI on your record you would have to report this DUI that they will see when requesting your CA MVR.