Hi Karin,
Welcome to the forum! Glad to have you aboard. I work in San Diego, so I have worked at La Jolla Playhouse (LJP), which is on the UCSD campus. What I can tell you is that they heavily favor their graduate stage management program. As an undergrad, you would have ample opportunity to be an ASM or a PA on the school productions, but the PSM/SM positions would go to the grad students. You could also apply to LJP to be an intern on their productions, but a summer show would be best as their schedules have day time rehearsals and would conflict with classes.
If you wanted to PSM/SM at UCSD, you might have to work on the purely student productions. So, what I can tell you is that you will get some experience, but probably not the whole package. I know that UC Irvine also has a grad SM program, so you may run into a similar situation there. For my two cents, I went to a small liberal arts school and was able to SM most of the shows. It was such good experience to learn the ropes of running a production without the pressure of it being professional. At UCSD, you wouldn't really get a chance to PSM until you were out of school. That being said, the productions are top notch and you would get to work with a great group of people that will become life-long contacts.