I may be doing a bit of “overkill” on mine, but, I do a little more. Dumping into drum and pumping out will take care of washing machine pump, but (unless you’ve thoroughly blown out the entire system) you will still have water in supply lines to washer. I pump through both cold and hot with the antifreeze, then pump machine empty. I’m probably wasting antifreeze, but it gives some extra “piece of mind”!
I generally only winterize the washer once per year, so I accept the additional cost as just another “operating expense”!