Like said above... true Closed Captioning using a .scc file is embedded into video stream and is accessed by a decoder on the viewing end. This decoder can either be built into a TV or its a set-top box. Apple's software DVD Player allows you to view embedded CC.
It sounds like you are really wanting subtitles. I've worked with closed captioning, but not subtitles. However, I'm guessing you need an application like Annotation Edit to either create your subtitles from scratch or translate your .scc file to a DVD Studio Pro subtitle format.