By design, the Drupal CAPTCHA module disables page caching for pages it is enabled on.
So if you enable CAPTCHA for user login and/or registration forms, those pages will not be cached. This is often acceptable.
However, if you enable CAPTCHA for comments, and have the comment form visible at the bottom of each node, then a big portion of your site's pages will not be cached in the page cache at all.
This means that every node will be treated as if the user is logged in, even though it is anonymous visitors who are hitting. This incurs a lot of PHP execution and SQL queries to the database.
So, even though you are using memcache for your page cache, the site would probably suffer.