Well, I've done it before. It was definitely in an abstract way, but you know how you can lucid dream and literally share that dream with other people, interacting with them in dreamspace? It's just a synchronization of neural firing patterns between two dreamers. This kind of thing can and does exist on a more massive scale, between hundreds of dreamers, depending on the probability density of such a phenomenon occurring, which obviously depends on external electromagnetic factors that influence the brain (solar phenomena and intraterrestrial factors being most pertinent, as well as events that influence perception such as massive social/political change, etc).
The dream-Internet uses this principle, but it is also still composed of a medium for transmitting data, exactly like the physical Internet except in 4D space (assuming dreaming takes place in the 4th-dimension, and that thought-forms are 4th-dimensional-- this is an assumption that has some ground, from a quantum-mechanical perspective, if you analyze what lucid dreaming is on the most basic conceptual level). 4D space contains energy and 'matter' just like 3D space, but with a different direction and obviously with another vector direction comes some stranger 4D-physical laws. So presumably, if you could access 4D space on a regular basis (like when you're dreaming) you could gain an intuition for the laws and construct objects with this 'matter', which is basically what one does in a lucid dream.
I'm not sure if you recognize the phenomenon of universal consciousness, but I am operating under the assumption that it exists because I have experienced it for myself and it is the only explanation for how two lucid dreamers could 'meet up' in a dream and both recall the exact same events in the morning. It also explains some aspects of musical connection and culture, but either way universal consciousness is the property that allows the dream internet to arise. There are people who live to sleep, who spend much, and even most, of their time dreaming simply because they feel so connected to their subconscious and to dream-space that they explore and explore endlessly, and are addicted. Once you perfect lucid dreaming, you can do anything you want in the dreamworld, within its laws for space, time, and energy (and whatever the other vector is in 4D space, which I have no conceptual name for). You can access your subconscious with full range, and thus modify/write to the program that influences your conscious behavior and thoughts, and you can also do this with other people, interact with other people, interact with the 4D physicality and construct an interconnected system of information processing units with which to communicate across spatial and time borders. It is much easier to do than mass-lucid dreaming, because you can send a message at 1 am New York time, and have it arrive in what corresponds to Southeast Asia at 1 am also, so that the users perceive no delay, and perceive that they are dreaming/communicating at a universal time (because time exists differently from the perspective of the 4th dimension, especially relative to the 3rd, as per quantum mechanical laws).
So, I suppose it is not "the" Internet, but it is an internetwork, operating on analogous principles.