noblepepper:
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.
Sorry, but that is wrong. The Leonardo has 2.5KB of RAM, while an Uno has only 2KB of RAM. That's theoretically 25% more RAM, but if that makes a BIG difference is a totally different issue.
The code space for sketches is 28KB on both (without tricks like omitting the bootloader)...
Ralf