A program could be written to do that- but the question is exactly why? Basically what you want is a folder where anything that is written there gets moved (not copied) somewhere else. Err.. why not just write the file in that target folder to begin with?
Then you mention that you want the program to possibly move to multiple folders- well that's not a move then that's a copy.
I could see if you wanted a program where based on the filename or attributes it would move to different folders, but to move every single file seems kind of useless to me.