Do that, and the speed won't work either. Basically, there's no way to stop the odometer from working without also making the speed stop working short of taking apart the gauge cluster and removing one of the odometer drive gears.
On an ironic side note, my E30's odometer recently started counting the miles twice as fast as it should be - my odometer and trip meter now put on exactly two miles for every mile that I travel. The speedo still registers the proper speed. Pretty strange. I don't care at this point, since the car has like 290,000 miles on it, but I can't for the life of me figure out why it would be doing this.