Engorgement does not need to happen.  Many times women confuse the natural
swelling of breast tissue by blood and lymphus at the beginning of
lactation, with engorgement.  If a woman is allowed to room-in and nurse on
response (so much nicer than "demand"), her engorgement should be minimal,
if at all.

I think engorgement is more likely in these hospitals that have restricted
feeds.

Nofia