While I can't dictate what orgs do, it'd be helpful to see some "we applied with zero connections and got in on our strength alone" posts to balance it out.
Here's one for you: https://twitter.com/joseluisnuno/status/770711984543244288
We were also unusual because we are probably the first Indian YC startup with on-ground operations. We went through 3 rounds of YC interviews (not just the one!) .. because the interviewers had to learn about India. Our first interviewer was mwseibel !
What impressed me was that YC learned about India, invested in us and supported us through a pivot back in India. Big shout out to Aaron Harris, who is probably the resident Asia expert now [1]
We hadn't ever been to Silicon Valley or to the United States, and no company from our country (Brazil) or even our continent had ever joined YC before us.
Having no connections is no reason not to apply.