I ended up looking it up after I posted, and you're right! Plans also include going all the way to the Santa Clara Caltrain station, surprisingly. Maybe by 2030.
From my understanding, most of the benefit of this BART extension will be for East Bay commuters (areas in the south, like Milpitas and Fremont, in particular) who are more likely to work in the South Bay than in San Francisco.
Caltrain presumably will remain the fastest option from San Jose, at least if regressive enclaves like Atherton don't delay the improvements for the high-speed rail project.
Getting the fiefdoms to coordinate is the Bay's eternal transit problem, however.
Oh certainly, the political implications of digging a tunnel under Los Padres haven't even begun to unfold.
I support the project, but part of me wishes that the money could have gone to massive improvements of Los Angeles, Bay Area, Sac, and smaller cities' transit (with density bonuses, value-capture schemes, etc.). No way that wins a statewide ballot though.
In the end, the Caltrain improvements as part of the project will help a lot, which I think include more double-tracking as well as electrification and grade-separation.