No. Because what you described is not a problem. No one has a need to ping cloudflare.com and HTTP access to sites behind the Cloudflare proxy has no relation whatsoever to one’s ability, or lack thereof, to ping cloudflare.com.
What you are describing is an XY Problem. You are sharing a symptom generated by an act that you think is the solution to your problem. Your description does not explain the actual problem that you think pinging cloudlfare.com will solve.
So I ask again, what is the actual problem that you are trying to solve?