If you want to see your website in Google you definitely have to ensure that SSL is presenting on your website.
Believe me, I'm telling it from my experience.
No that's not what happens, if your site does not have an SSL cert then anyone visiting the site will get a 'This site is not secure' message.
Google and Firefox are just giving priority indexing to sites with an SSL cert.
Did you face this problem?
I had no such case you are talking about.