Can you wait until after the annual fee shows up in a statement before cancelling a card (will they always refund the annual fee?) or do you cancel the month before the annual fee shows up?

I made a mistake in cancelling a United Mileage Plus Visa before my statement w/ the annual fee showed in a month that I made a lot of charges, and forfeited all the points which hadn't posted yet plus forfeited all the "bonus" points that I was suppose to get much earlier but never did They kept wanting me to switch to one of their zillion other cards (mileage earning & otherwise) --- but I didn't & wonder if I did switch accounts (vs cold turkey cancel) if the miles would have finished transfering?? Anyone know?

I really am just wondered if some places will refuse to refund the annual fee once it posts if you cancel after the fact...