Yes, our washer hose drains into our deep/laundry sink as well. Works great for us.
Our basement laundry sink is the drain for not only the washing machine but also our HVAC system.
At our first house, the basement washer drained into the laundry sink. (I seem to recall a panty hose strainer at the end.). When we added a dishwasher to the kitchen, hubby proposed running the drain hose down there too. I said NO - didn’t want food crap going down the laundry sink.
We have an old house with plaster walls, so only some rooms have A/C and the unit is in the attic. It has a drain pan, but it drains via a small pvc pipe that comes through the ceiling of our main 2nd floor bathroom maybe 12” or so over the sink. With 10.5 foot ceilings, it’s not as noticeable as it sounds. But it has a couple of bends in it, so it looks like a snake. We sometime joke we should paint it as such.
Over the years the unit has gotten stopped up a few times and also broke, and liquid did drip through. At least it was hard to miss that something was wrong up there