Below I have listed the expected results when using the Call & Message Block(CMB) feature within your My Verizon account.
If a number you've blocked attempts to send you a message, you will NOT receive a message; however, if a picture message is sent to you by the blocked number you will see the title line of the message.
Blocked line outcome (from a VZW customer)- If you've blocked a Verizon Wireless number, the sender will see a red X in the sent folder with status failed notification "Delivery failed. Invalid destination or service blocked at destination". Also receives a text message alert - "You cannot send messages to destinations that are blocked by the account owner."
Blocked line outcome (from a non VZW customer)- The sender will see a green check mark with a "message sent" notification but message will not be delivered to you.