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It depends what you're doing and where you want to work, but it's competitive: you're going to need a technical degree with a very good grade average to get in the front door at a lot of companies. Systems engineering and physics will probably stand you in very good stead.

I'm not in silicon valley, but just a question for your question: If you want to do any kind of hot-shot software development as a career, why would you study systems engineering and physics? It seems like an oblique way to go, kind of like getting a statistics degree if you want to do pure math research. Within a CS degree there is also a lot of room for your own interests, many of which are highly quantitative.

More important if you're going through HR. Less important if you're networking.

Also, I know and know of gobs of people in CS who were educated in physics.

It's important if you want to get a job. Not so much if you want to start your own business (see my other comment in this thread for more details on that.)