curl request via Nginx with mTLS enabled

When Nginx is configured to verify server's TLS chain like this:

  proxy_ssl_trusted_certificate some.pem;
  proxy_ssl_verify on;
  proxy_ssl_verify_depth 3;

and testing using a curl command, will both curl and Nginx perform server TLS chain verification?

Assuming curl makes requests through the nginx proxy (using -x/--proxy if HTTP inside TLS; --proxytunnel for other protocols) then yes, both curl and nginx are verifying the server certificate by constructing a chain from that certificate to a trusted root certificate. If you don't want curl to verify the certificate chain, you can use -k/--insecure.

EDIT: If your concern has to do with mutual TLS (i.e. curl is sending a client certificate to the server) then please edit your question to make clear your concern about mTLS. I did not consider mTLS to be relevant to the question because you asked

will both curl and Nginx perform server TLS chain verification?

(emphasis mine)

mTLS certificate validation/verification would involve the client's TLS chain.