The essence of engineering is to find the most economical way to satisfy the functional requirements while ensuring safety and all that stuff. Just make sure the washer drain is adequately secured so you don't flood anyone downstairs.
Now I'm sure there are lots of reasons such as the fact that it isn't permitted by the Universal Plumbing Code, but I can't think of a technical reason that it wouldn't work fine. Just don't tell anyone in your condo about it. And make sure that you regularly check the tub drain to make sure it doesn't plug with lint and overflow on the fourth load.