It usually does with Mercury. But Mercury writes business under at least 3 different company names in California, and polices change from time to time. You need to know the policy edition, the issuing company, and in addition to being listed as a driver on the policy, you need to know whether or not the proposed driver is the named insured, a relative of the named insured, or a non-related, but listed driver (such as a roommate).
In general, if the person is a family member of the Named Insured, is listed on the policy, and resides in the Named Insured's Household, then Collision, Comprehensive and Liability coverage should transfer. If the driver is not a family member, but is still listed on the policy (roommate) I would not assume coverage without reading the policy form or knowing exactly which policy you are dealing with.
New business policies will likely cover a registerred domestic partner of the Named Insured, as well as non-family members (so long as they are listed on the policy and reside with the Named Insured) but some older Mercury policies will not.