Is Drupal contact form securely encrypted?
No. No form, in any website, is inherently "secure" or encrypted. If your requirement is to serve and submit the form over TLS, you'll need to set that up on your server/host as a separate task.

Once you have, Drupal will happily serve any page over https, and submit forms in the same manner.

The only thing you might want to consider from a Drupal point of view is to un-comment the lines in the default .htaccess which force-upgrade all requests to https. If your server isn't Apache that'll have to be done elsewhere.