Yes and No!
It depends on whether your baby is breastfeeding or bottle feeding. Milk can really pour out of bottles and babies have to gulp to keep up. When this happens babies will often drink more milk than they really need or want. It takes 20 minutes for the message to get from the belly to the brain so if your baby finishes his bottle in 5 or 10 minutes he may want more because he doesn't know he is full. Newborns need lots of sucking time which they typically get while breastfeeding.
If you are producing lots of milk and you hav a very fast or overactive letdown, your baby may also drink too much in an attempt to satisfy her sucking needs. Try to slow down the flow of milk by lying on your side to feed or by applying some pressure with the palm of your hand to the side of your breast.