If you use the extension send to chat API you are rate limited to 12 messages per minute.
If you use an extension to send messages to a chat bot to send to a chat channel, then normal rate limits apply and moderators of the target channel are liable to apply the channel rules as they see fit. if the bot is also a channel moderator then only a broadcaster can moderate the bot.
If your bot sending the messages exceeds the chat rate limit then it’ll get globalled for a brief period of time. Usually this only happens on a malfunction.
So
No this shouldn’t happen, a ban from Twitch shouldn’t happen