IPhone and iMessage service?

So, I have an iPhone 4. Since the battery sucks, I usually have the internet and the iMessages disconnected.
But I'm not sure what happpens if other iPhone users send me an iMessage when I have the service turned off. Do I still get them? Even when the internet is on and the iMessage is off?

That shouldn't affect the battery at all, mine is always on and the battery life is great. I haven't' turned imessage off since the day I bought it.
Obviously if you are messaging for 3 or 4 hours it will use battery.