Yes, you are very correct in saying that you would rather have a portion of money left over.
When you get into road biking, you will eventually have to spend money on maintenance and spare parts. Every 1500-2000 miles you've gotta replace the chain. If you have a good cassette, I think it'll last you until you're out of college and have gotten a job, but they can last up to 20,000 miles with good care.
There are some optional things you might end up buying, such as cycling clothing, shoes, and pedals. These can be expensive, but most people who get into serious road biking will buy them eventually.
It hurts me when a bike like that is called a "power climber" since road bikes are much lighter and will climb better. Since you're a college student, getting a brand spanking new road bike will cost you more than $500. I highly recommend working over your summers so you can save up some more money. There's nothing inherently wrong with the bike you have now since you can still use it to get a good workout, so I would say it's OK to wait to save up.
I'm a college student as well, so I've got to be on the lookout for deals and stuff. What college do you go to? Does it have a cycling team? Some college teams can offer students good deals on bikes. You also might want to consider getting a used bike. You can find good deals on craigslist, but make sure the bike fits you. At 5'4'' you would probably need a small frame, maybe a 50cm or 52cm frame, or even a 48cm. This measurement is of the seat tube of the bike (the one you're sitting on). But the size you need will vary depending on the geometry of the bike, but I would ask your local bike shop to be sure. Make sure they guy you're asking is an experienced bike fitter and not just some salesman looking for a commission.