Is it possible for an undergrad to publish in a journal without conducting experiments (using existing data)?
In principle this is possible, however, when using data collected by somebody else you have to take great care not to produce bad science. Data collection is usualy performed with a certain specific application in mind, and when collecting data you have to make sure that the errors introduced in the collection process do not influence the final result in a way that is important for your purpose. If you use the same data for some other purpose your results will likely be affected by some bias. 

So if you want to corelate oil prices with GDP growth, you are fine, but with more complex questions you are in real danger.