Not quite but generally with start-ups the person you need to speak to is ridiculously busy so you will simply struggle to get 5 minutes of their time.
Depends on the size, but I've found startups pretty responsive via email. I haven't asked for a job, but I'd imagine there's a good chance a real human will read it, and might remember you if your skills are relevant and they later need someone in that area.
I don't think you need to actually get a hold of the person you want to talk to on the phone. Simply initiating contact like this outside of a job posting will show that you are extremely interested.
