As far as I know you can’t use VSE strip as input, but you can render it as image sequence and in compositing add -> input -> image, select first frame of your sequence, change input type from file to sequence, set number of frames, start frame, then do your nodes stuff and render.
There are lots of old requests for round tripping strips to the Nodes, or making them an effect strip to apply in the VSE. Alas that is not the case as Comp Nodes are the end of the rendering line in Blender.
Look forward to Project Mango as it may be a project coding task, depending on their needs. As it will involve a lot of camera footage (not just animation) they may want to solve the colour grading issue in a more elegant fashion.
Just select a still frame media type, like png or jpeg (not AVI JPEG) and Blender will render the range of your movie (without sound) as a series of frames with incremented numbers appended to the name. Later you can re-import these and Blender will turn them into an animation.