This question is, in part, inspired from the 1997 Hollywood movie Volcano, where a fictional volcano erupted out of the La Brea Tar Pits in Los Angeles.
The San Andreas Fault is a transform fault plate boundary (see image below):
Image from the USGS Glossary entry for transform faults, with a definition:
A transform fault is a special variety of strike-slip fault that accommodates relative horizontal slip between other tectonic elements, such as oceanic crustal plates.
A specific type of transform fault is a 'leaky transform fault', which according to a source used on its Wikipedia page describes the tectonic movement at this type of faulting as being:
In addition to the regular strike-slip motion observed at transform boundaries, an oblique extensional component is present, resulting in motion of the plates that is not parallel to the plate boundary.
Is there any evidence that oblique tectonic movement occurs along the San Andreas Fault?
Hence, is a San Andreas volcano possible?