If I have the following set-up, would the sound output be played and used as sound input? I haven't got a splitter yet, but I'm just curious whether this would work.
I do not believe this will work, mostly because of the chicken or the egg problem. If the input is coming from the output, and vice versa then how does one start from nothing. There is no initial input and no initial output. Unless you hooked it up and injected some sound from outside the loop to get it going.
Well, both the output and input are the standard out- and input from my computer. All I want to do is feed the output back as input so that I can, for example, record the sound of what's playing on my desktop or, when in a video chat, make people listen to a song "directly" from my computer.
It's similar to how feedback with an electric guitar works. The strings vibrate which generates noise which is amplified by the amplifier which makes the string vibrate more which is amplified by the amplifier which makes the strings vibrate more... ad infinitum. Obviously you need something to make the strings vibrate, or in your case, output, but yes, it will work; but like xander337 said all you're going to get is feedback.
You could do this in audio settings, except with no splitter.. looping the output into the input virtually.. although I don't think you could use headphones along with that :D
EDIT: err... maybe actually...
If your using Linux then I could tell you how to make it work flawlessly, windows I'm not too sure about... although I have friends who have had success..