I changed from BT openworld some seven years ago and yes I did lose my account almost instantly - If you think about it - you are no longer a customer - so why should BT continue to do anything for you at all ?
So the answer to your question is YES you will lose your mail accounts at switchover - so make sure that any account dependant suppliers (Gas, Electricity to name but two) are aware of your new ISP - Otherwise important info (bills etc) may go astray