Can someone send a text message after Apple 6 is set to refuse to answer the phone?

You can still receive it. You refused to answer the phone instead of texting. Refusing to answer a phone call and refusing to answer a text message are two different things.

Now the management software of the mobile phone can set the rejection of incoming calls and short messages, but it will still prompt the rejection of short messages and incoming calls. It is of little use to refuse text messages, but it is still good to refuse calls.

Apple has a "SMS blacklist" function. If you want to reject his message, you can set-information-blacklist (bottom)-information. Then add will pop up the phone address book and select the name to block.