The short answer is Yes. The reason is simple, while some vulnerabilities requires Administrative privileges, other vulnerabilities bypass the UAC mechanism that prevents unattended elevation to Administrator privileges so combining the two creates the risk.
I know this is not the answer your want, but from a security perspective, the right answer is removing admin privileges and granting them more specific permissions if needed. Giving your users full admin rights are the best way to a full ransomware outbreak and other fun stuff you don't want to live through.
Unfortunately, you're probably living in the ...
The first error was because s_client doesn't like to see the root CA in sent in the TLS connection. The second error is because s_client doesn't trust the root CA.
To solve this second error, run s_client with the -CAfile option and specify the root CA.