No, Twilio SMS is a pay-as-you-go feature just like voice minutes. You are only billed for SMS messages that you send or receive with your Twilio numbers.
SUPPORT.TWILIO.COM END OF LIFE NOTICE: This site, support.twilio.com, is scheduled to go End of Life on February 27, 2024. All Twilio Support content has been migrated to help.twilio.com, where you can continue to find helpful Support articles, API docs, and Twilio blog content, and escalate your issues to our Support team. We encourage you to update your bookmarks and begin using the new site today for all your Twilio Support needs.