No. If Twilio returns an HTTP response error, this means that Twilio is unable to process your request and thus you will not be charged. Your request may be rejected due to a variety of reasons. Check out the error and warning code reference page to learn more.
Note that Twilio charges for the attempt of delivery, so any message marked as 'sent', 'delivered', or 'undelivered' in your Message logs will be billed to your account. In some cases messages may be sent from Twilio but are not received at the end user's handset. Check out our SMS troubleshooting guide for detailed troubleshooting steps.