Hi @bobn1029 Welcome to the forum!
EDIT: To answer your title question YES LetsEncrypt Certs will work on centos 6 server but OBTAINING the cert may be the real issue.
Thank you for posting the output from your renewal attempt.
There are a few IMPORTANT issues here presented by the certbot-auto script:
Certbot-Auto is depreciated and in addition to that, CentOS 6 reached it's END OF LIFE in November 2020.
So my recommendation would be to update your server to a level that is supported and maintained with security patches and other updates. (LTS releases are helpful)
Then you can install certbot or some other ACME client like acme.sh for example and continue to obtain certificates for your website.
I believe it would be a huge mistake to avoid taking the time to get your system up to date.
CentOS 6 is now End of Life and there are no more updates
https://certbot.eff.org/lets-encrypt/centosrhel8-apache
Hope this helps.