Yes, and it works perfectly fine, and nobody is going to care about your certificate authority.

CA (Certificate Authority) matters for the people, to enhance their customer's trust level for the business.
No it doesn't, please cite your claim that CA influences consumer behavior. Anecdotally I have never took a remote interest in whatever CA a certificate was from, nor am I aware of anyone who does.
This resource
http://abt.cm/1pfDRsW will help you to know 'how CAs enhance customer's trust'.
And if talking about which CA (Certificate Authority) or SSL Seal people trust the most in the last year then you should check this report http://[Suspicious link removed]/1eC64qf
I hope this will help you.