You can certainly do this, and you don't need an agent either. Most publishers will consider non-fiction book proposals along the lines you describe. Even new writers can have proposals accepted, though it obviously helps if you can demonstrate some sort of publishing record and/or expertise in the field concerned.
There is actually a lot to be said in favour of this method. As well as saving you some work (if no-one is interested in your book), if a publisher likes your idea, they may have specific suggestions as to how the book should be written. They may even be able to help you with it.
Unfortunately this approach cannot normally be used with novels, unless perhaps you are a well-known, successful author already. For most of us, if you want to sell a novel, you will first have to write it!
Nick
