If the baby falls asleep quickly at the breast, you can compress the breast to continue the flow of milk . Contact the breastfeeding clinic with any concerns, but wait to start supplementing. If supplementation is truly necessary, there are ways of supplementing which do not use an artificial nipple. This means nothing and should not influence you. Therefore, you should not pump 'just to know'.
Most mothers have plenty of milk.
The problem usually is that the baby is not getting the milk that is there, either because he is latched on poorly, or the suckle is ineffective or both. These problems can often be fixed. The baby will take a bottle after feeding. This does not necessarily mean that the baby is still hungry. This is not a good test as bottles may interfere with breastfeeding.