Phone goes to voicemail but messages get delivered blue?

Is it possible for an iPhone to be off but messages get sent blue and delivered anyways?

Sure if the person is still using other iOS devices to send and receive iMessages, other than an iPhone. Tablet, Computer, laptop, iPod Touch, etc.

Who knows

If you're asking whether or not the phone will still receive the text message when it's off, then yes it will still get the message. However, you will not know about it until you turn the phone back on