Does Secure Pages work with .htaccess non-www to www Redirect?

My Drupal 7 install redirects all non-www traffic to www via the .htaccess file (Apache/2.2.15). I believe me production .htaccess configuration is what ships with Drupal 7.

RewriteCond %{HTTP_HOST} .
RewriteCond %{HTTP_HOST} !^www\. [NC]
RewriteRule ^ http%{ENV:protossl}://www.%{HTTP_HOST}%{REQUEST_URI} [L,R=301]

Does this cause any issues for Secure Pages running in mixed HTTP/HTTPS mode, or was it designed and implemented to work with non-www to www redirection in mixed HTTP/HTTPS mode?

Thank you in advance for any help!