No, this is not possible.
When you fail to board your flight at A, the airline will cancel your entire itinerary, and will not allow you to board at C unless you buy a new ticket.
If you wish to fly only from C to B, then you should contact the airline in advance and change your booking. The cost of this depends on the airline's policies and the type of ticket you purchased. Typically it will be at least the difference in fare between your original ticket and a new ticket C-B, possibly plus some change fee. (If C-B is cheaper than A-C-B, you may be eligible for a partial refund or voucher toward a future flight; however, in some cases, C-B may be more expensive even though it's shorter.)