It isn't necessary to start with live sand, or live CC in your case. The sand/gravel will eventually become live on its own, just not fast. Using live sand has definate benefits but its use is not a must.
When you look at the technical side of it you'll find that sand offers a larger 'surface area' for the colonization of bacteria which makes it appealing for many, if not most, hobbiests. There are benefits that CC offers that sand does not, but the main focus with any substrate tends to be on biological filtration.
Biological filtration, which relies on nitrifying bacterial colonies to consume and convert wastes in the tank environment, work more effeciently with larger colonies. Large populations will need lots of realestate to colonize, which is where the substrate comes in. These bacteria do not swim freely through the water, they settle on porous surfaces like the substrate, decor, filter media, piping and powerheads, etc.
You can safely fit more sand/gravel in a tank without disturbing the environment than you can decor, powerheads, filters, etc. so the main focus on substrate becomes focused on its ability to support better biological colonization. Crushed Coral gravel will work just fine, and theres nothing wrong with using it, but the sand will work better because of its ability to support larger bacterial colonies.
The way I would describe it, which is not at all scientifically backed (more like my guesstimation.

), is a 1" bed of sand will give about the same filtration capability of a 3-4" bed of CC gravel.
Although many people like to rely on their filtration equipment for all of their filtration needs, including biological, it is my opinion that having a colonized substrate is essential to ensuring the continued stability of your aquarium. Filters with biological media included are all well and good, and will certainly contribute their part to the extraction of waste, but these should not be relied upon to shoulder the whole burdon on its own.
HTH,
Aaron