Does imessage say text message if the iphone is off?

Hopefully someone who knows about the iphone can answer this. IPhone to iPhone usually says "iMessage" when you text(blue send button).So lets say your phone dies or it is off does the person texting you still see "iMessage" or will it change to "text message" since the phone is off?

No. It will still say iMessage.

Yes! It will send as a text message when the other phone is off. It will also send as a text if the other person doesn't have signal.