No, neither your text messages or your Sideline calls will show up on your phone bill.
However, you will see two numbers on your bill related to your Sideline account. These are your pilot numbers (Inbound and Outbound). These numbers can be found in your device's contact list/address book (under Incoming or Outgoing Sideline Call). These pilot numbers connect your inbound or outgoing Sideline calls through your carrier network, which is why these will be displayed.
If you need more information, feel free to email us!