The trend in the industry has been to more openness on this question recently, in no small part driven by YC, which basically pioneered investing at scale in companies without requiring a social connection.
Also, quick fact of life in entrepreneurship: there are many ways to skin the cat, but if you are hypothetically in a situation where the business needs connections, then the job is going and getting connections. If you e.g. take a random named person with checkwriting authority in Silicon Valley, and ask "How many people have social permission to introduce me to this person?", that answer is likely in the high hundreds to mid single-digit thousands. Substantially all of those people have an email address. Many of them respond to emails very quickly, particularly when they're interesting. This suggests that the immediate problem is less having elite connections and more organizing your life such that you send an uncomfortably large number of interesting emails.