The Yun has two processors talking to each other over a serial link.
The micro controller side is like a Leonardo which has LESS ram than a Uno, so no you can't run your code there if you run out of ram on an Uno.
The AR9331 runs linux but you can't run "sketches" there any more than you could on a desktop running linux. You could PORT much of your code but this is not a simple task.