What does Apple do with this information?

Apple do not state what they do, otherwise scammers could try to circumvent the guidelines that Apple release.

I suspect they block or close accounts that infringe the terms & conditions of the Apple ID.

Also you need to be careful with the type of message, SMS is different to iMessage. 'Texting' normally refers to SMS only. iMessage may not be using the phone number (it needs an Apple ID). SMS does need a phone number.

Apple doesn't block SMS's on other peoples phones if you report those messages as far as a I can tell.