Before you decide to use it, first check to see what kind of cable it is. Unscrew the wall plate with the F-connector and pull enough coax out to see the markings on the jacket. If it says RG-59, RG-59/U, or something similar, it will support composite video. If it says RG-6, RG-6/U, etc., you probably don't want to use it for that application.
The reason gets a bit technical, but basically, RG-59 has a solid copper center conductor, with a pure copper ground braid; while RG-6 is made with a copper-clad steel wire, with an aluminum foil & braid shield. Because RF frequencies travel more along the "
skin" of both the center conductor and ground braid, it doesn't mind that below the copper clad of RG-6 is a rather poorly conducting steel wire. Composite (or baseband) video is much lower in frequency and travels more through the core of the wire and DOES mind having to plow through steel. For short runs, it probably wouldn't matter, but if you are taking it any distance the loss will eat up much your composite signal before it reaches the other end.
Just a head's up before you put too much time and effort into it.