Not Legal Advice:
According to the California Department of Alcoholic Beverage Control, as authorized by the California Constitution: Rule 143 CCR -Employees accepting alcoholic drinks can result in a 15 day suspension of the establishment's liquor license, so no, a bartender can not drink on the job.
Additionally, according to 24200(a) B&P - a Licensee or Bartender Working In Premises While Intoxicated may result in a 30 day suspension of the establishment's liquor license.
You can read more about how these penalties are handled, along with the many other rules that may result in license suspension at abc.ca.gov.
If you're thinking of applying for a liquor license in California, some helpful tips can be found in PermitPlace's article California Liquor License: Five Questions To Ask Before Applying.
In the news for those of legal age that want a drink but don't feel like leaving the house, The Alcoholic Beverage Control Board has lifted its ban on booze delivery apps and services.