I know proper frame sizing is preached here, but what happens if you ride a smaller frame? I'm a good 6'0 and have ridden a ~52cm bike (it was free...) for the last three years. Now I’m in the market for a new one but since I’m still a student I can't afford much. There is a good 55cm road bike in my budget range and I am seriously considering purchasing it for commuting and weekend warrior trips. Am I going to seriously damage my body (back especially) continually riding small frames? Thanks

Late in the 19th century, a physician in Austria warned against all bicycle riding on the grounds that riders could develop what the good doctor called kyphosis bicyclistarium - the dreaded "cyclist's hump." While this proved to be bunk, the warning was picked up by the popular media and became another die-hard bicyle myth. You're not going to do damage to your back riding recreationally on a bike too small for you.

However, why the question? Sounds like you're set to buy the 55cm bike, which almost certainly will be a better fit for your 6-foot body and allow you to ride longer in a bit more comfort and ease.

You could always go to a longer stem and bars with more reach if needed as long it's not to the extreme where it would upset the balance of the bike.

You already know the fit lecture: It's the most important thing, never buy a bike that doesn't fit, etc. etc. It's good advice...but a lot of us began riding back when $5 was a lot of money to us, and you don't always get to choose your equipment. You're presumably a young guy, infinitely bendable (that will change, just you wait) and I can't see how you'd do any permanent damage by riding a bike that's too small under the conditions you mentioned.
If you decide to look for a longer stem or seatpost to adjust the fit, don't ignore thrift shops like the Salvation Army or whatever's in your town. They rarely have bike PARTS, but they often have whole bikes you can cannibalize. For two examples, I bought a Specialized Hard Rock for my wife for $10 and a Centurion LeMans for my son for $25. The HR was a low-end mountain bike from the '90s, but she only wanted it for a beater and it came with a $40 Blackburn rack, $35 Avocet computer and an REI seatbag with patch kit and tools.
The Centurion was the real steal, though. It was a nice lugged steel bike when it was new, still in good shape, and came with barcon shifters and a Brooks B-17 saddle, easily $150 just in those two items. We're riding them pretty much as we got them, but there were other bikes there for less than $25 that could have been stripped for wheels, bars, stems, whatever.

I'm virtually certain that the Schwinn varsity that got me through college was completely the wrong size. Good news is that a 20 y/o body is resilient, and hey, money is an issue.

I couldn't really fault you for going that route.

just a quick note. I am 6' and ride a 56cm roadbike that fits perfectly. If you have a proportionate physique, I would guess the 55cm is pretty much close to what you need anyways..