Hi jpark9,
No, the experiment will not work without ammonia and oxalic acid. Take a look at equation 1 in the background information. If you took out ammonia and oxalic acid, then the only reactant that would be the iodine. So, the iodine would not convert to iodide.
Photochemical reactions are very important in Earth's atmosphere, where they are responsible for breaking up ozone molecules. The free oxygen released in the process can bond with hydrogen to make hydroxyl radicals. Photochemical reactions are also important in the atmosphere of Titan, one of the moons of Saturn. On Titan, photochemical reactions produce organic compounds. Photochemical processes are also important in manufacturing. Check out this Wikipedia article for more details:
http://en.wikipedia.org/wiki/Photochemical_machining