No. You lose your MR points when you cancel the card - although I think there is a 30 day grace period (definitely don't trust me on that). The way around it is to apply for a free Amex which has MR as a benefit, should such a card exist. Or spend them!
The grace period is there mainly to help people who have corporate MR cards and who get fired - it gives them leeway to apply for a personal Amex and keep the MR points alive.
Will amend OP.