If both you and the person you are texting have iMessage, and that person's phone is dead... Will it/Can it still be sent as an imessage? I am getting different answers from people. I want to know if this person was being untruthful about there phone bein

Is Settings>Messages>Send as SMS set to "on"? If so, the message will be sent as an SMS if iMessage is unavailable. Unavailabe could me the phone was off or not connected to cellular data or WiFi.

IF that is the only iDevice activated for that recipient, then no. It should not successfully send as an iMessage if the phone is powered off or has no data connection. If you have Send as SMS turned on, it should automatically fallback to SMS after a few minutes. Of course, they won't get this until they power on their phone, assuming they have a text messaging plan with their carrier.

iPhone, iPad, iPod Touch, Mac with Messages Beta running... if iMessage is activated on multiple devices with the same Apple ID, messages to/from that Apple ID will be synced across all of those devices.

iDevice means any device that uses iOS which would include iPads, iPhones and the iPod Touch.