Don't display custom field if it's empty

If you’re referring to the manager, then no, this is not supported (such a behavior would not be sensible because you could never add content to that field if it were hidden). If you’re referring to the front-end, then there are lots of ways you could do this — write a PHP if statement in your template, or use one of the CCTM’s output filters as a convenience method to do the same. See https://code.google.com/p/wordpress-custom-content-type-manager/wiki/default_OutputFilter and https://code.google.com/p/wordpress-custom-content-type-manager/wiki/wrapper_OutputFilter