I don't have a Linkedin profile. What's suspicious about that? Or do you mean just in the context of cultivating that network? If so, how would you know given that there is no nexus to that network?
Depends on what you're looking for. Many of the best don't have their number in public, and they are not going to answer random calls from unknown callers because they're busy doing important or interesting stuff. But yeah, you probably can't approach them on LinkedIn either.