Yes, but the booking class can be manually overriden or changed by the airline agent attempting to reaccomodate you. And the more rushed they are, the more likely you will be booked in a higher fare inventory since it's generally faster and easier than hunting and pecking for space in the originally booked inventory.

Some airlines are "good" (at least to the customers redeeming miles) while others are "bad" in this regard. BA is "bad" here: they try very hard to make sure that reaccomodations don't result in additional miles/tier points.