The manner in which security questions are used by a site, determines whether they undermine the supposedly stronger authentication mechanism (of using good passwords).
Typically, systems that allow access to users after they've answered a security question, are weaker than systems that would communicate a (temporary) password to the user via a (different and secure) channel. The previous statement conveys a best practice, and certain systems need not implement all of it; some systems would provide a new password (which need not be changed by a user), and there are other systems that would communicate the password via an insecure channel.
Filling a security question with random characters is not necessarily a good approach (although it is better than having a smaller answer with low entropy), for it would make it difficult to remember, resulting in a potential lock-out scenario (from where this is often no point of recovery). It should be remembered that security questions are often not changed periodically unlike passwords. The answer therefore depends on how well the answer is protected (both by the user and the system), how public the answer actually is, and how frequently can the question (and answer) be changed.
Reading this related StackOverflow question is recommended, for the answers discuss out-of-band communication, amongst other issues like the potential lock-out scenario.