Overdue date might be caused by umbilical cord around baby neck ?

( I am 41 weeks pregnant now and nothing happends. I have an appointmen to be induced in 5 days from now.The midwife said the baby head is engaged 3/5 but when i have been in hospital the doctor said is not engaged.) I wonder if the baby might not go down because the umbilical cord might be wrapped around the neck and this to cause a late arrival ? Did anybody had a similar experience ?