No, unblocking someone on an iPhone will not change the label of the text input field where you type messages. The label will remain the same, displaying "iMessage" when you are sending a message to another iPhone user using Apple's iMessage service, and "Text Message" when you are sending a regular SMS/MMS to a non-iPhone user or when iMessage is unavailable.
The act of unblocking or blocking someone only affects whether you can send and receive messages with that person, but it doesn't have any impact on the user interface or the label of the text input field.