Indian Exit permit- could it be skipped? how quick its issued?

Asking on friend's behalf - Any experience of departing from Indian airport without Indian exit permit. Child born in India and Both are UK passport holders & OCI card holders. After long wait Child's British passport is being issued & on its way to India. They need to depart India as soon as the passport arrives & wouldn't have time to apply & wait for couple of weeks for Indian Exit Permit to arrive..
They've a proof of child having no claim to Indian citizenship .
1) So, what will happen if the family just turn-up at Indian airport's immigration counter without Indian exit permit? Will they be able to depart ? They're ready to pay any reasonable fine which is generally levied on foreign child born in India.

2) Could they apply to FRRO & without waiting for exit permit to arrive, depart for the UK?

Please advise
Cheers,