Relative paths are accepted as the destination of message_type 3, but beware that the root directory is determined by the context of the call to error_log(), which can change, so that one instance of error_log () in your code can lead to the creation of multiple log files in different locations.
In a WordPress context, the root directory will be the site's root in many cases, but it will be /wp-admin/ for AJAX calls, and a plugin's directory in other cases. If you want all your output to go to one file, use an absolute path.