CAW question: Will CC export with world?

I've been alternating from working on my world in CAW tool and going into the game and making some builds. I've realized now I've made a bunch of homes with CC. When I finally finish my world in 2027 (seriously so much work!!) and export it, will the CC just download with the world like builds from TSR do? Because that's how I have got most of my CC, not links, just came with builds I've downloaded from TSR so I have no way of sourcing it or providing links to downloaders. And I don't want my world to look like shit with things swapped in place of CC.

Any idea?