I think that the opportunity to increase your research exposure within a more structured academic setting via the post-bac program could be a real boon to your subsequent PhD apps. The faculty at Berkeley is world class - getting a letter of rec from one of them would certainly look very good (assuming they genuinely get to know you and your work, and assuming you do good work!). And, of course, if you make use of your time there, and can create some products (e.g., publications, etc.), that would also help! I think it's what you make of it. I agree with erg923 that doing the program in and of itself might not be helpful (like -- on your CV, it would weigh more to have a high impact journal publication, per se, than simply having completed the post-bac) but if you are able to take advantage of the opportunity to really immerse yourself in research, develop a research plan and a better sense of what direction you are headed for grad school, etc. then the post-bac could be really helpful! I think of the post-bac as kind of a "second opportunity" to build your CV and research chops, if for any reason you didn't get to do that previously (e.g., you majored in something else in college, you are changing career paths, etc.)
That said...I don't think a post-bac is the only route to gaining the experiences necessary for entry into a good PhD program! You could get similar experiences by volunteering in a research lab, undertaking independent research, etc. However, I do think that the structured, intensive, and supportive nature of the post-bac is probably a nice, protected environment in which to really dedicate yourself to doing what you need to do to get into a PhD program subsequently.
My two cents.