Please watch this short video and let me know if and how I could have the page section elements recognize the added editing power and capability of visual composer the same way regular WordPress pages can.
You should be able to use VC with page sections by enabling support for that custom post type in VC settings. Last time I checked, VC frontend editor was loading some scripts which conflicted with those of theme.
Why not use the shortcode builder instead? If you use VC, it can be hard to use the visual editor to view demo source code since it messes up the code there making it virtually unreadable.