If your water is from the same source as anywhere else in the house, then I say yes. If you live in an area where the water for your washing machine is "non-potable" then I say no.
In my nearly twenty years experience installing residential plumbing I have never heard of anyone using gray-water for anything other than irrigation. Some commercial buildings use treated gray-water for flushing toilets, but nobody would ever consider using it for laundry. They call it "gray-water" for a reason, it would not give you very bright whites!
I have plumbed houses where the softened water went to the washer-box, showers, dishwasher, et cetera. There is some debate as to whether softened water is good for drinking (and hence fishkeeping), so this is the only reason I could see that would make the laundry sillcocks a bad idea.