Should be wide enough for a dryer to set under. Don't see a washer and dryer both being able to be under it though. It should be stable enough with the two shelves mounted above as well. Just use the casters instead of the wheels and shouldn' t have any issues reguardless.
It may be a bit unstable , though, since there will be such a long stretch from the shelf to the floor. The shelves provide rigidity to the structure. When you're first assembling it, the legs are pretty wobbly at the top until you get a few shelves installed. There may be a way to make it work for your purposes, though.