Depends on the seller, their ugency to sell, and the validity of the list price!
I would say that, in general, most sellers won't jump up and down clapping their hands with glee with an offer 20% below their list price, cash or no cash.
That being siad, if the house is overpriced and has been sitting on the market for a while.........then you might be able to work something out. Just make sure your agent has smelling salts when the offer is first presented!
Kidding aside - if the home is reasonably priced.......it's unlikely $400,000 will work......but.........you have nothing to lose! Give it a try!
(what does your agent have to say, assuming you have one??)