Will text messages be sent after the broadband real-name is passed?

Yes

After the real-name authentication is successful, you will usually be notified via text message during the authentication process.

Within twenty-four hours. Now after the real-name authentication, the text message will basically come immediately, and it will not exceed 24 hours at the latest. If your broadband application is successful, staff will come to your door to install and debug it. If you do not receive the information, you can also call customer service to ask when staff will come to install it. If you have applied for China Telecom's broadband, it will usually be sent to your reserved number via text message within 24 hours, so that you can use the broadband you applied for to access the Internet.