Bad idea. You should be decreasing 1) the reliance on liquids for calories, and 2) the reliance on bottles if he is over the age of one. You may not want to do it, but try sleep training if he is up hungry at 4am. And/or shift his meals, maybe adding an extra snack, so he gets a final meal of solids and milk (in a sippy cup) at 7:00-7:30 before the 8:00pm bedtime. I’m theory, that would have him sleeping on a fuller belly and could buy an extra 2 hours of sleep.