Yes, a fishless cycle could have prevented your fish from coming in contact with dangerous levels of ammonia and nitrite. (Of course at this point it's too late for this method since you already have fish in your tank.) There are several good links in the treating and avoiding new tank syndrome sticky thread you should take a look at. Essentially, you add a source of ammonia (bottled household cleaner, need to ensure it is only water + ammonia, no detergents or perfumes) until the ammonia level tests at 5ppm. Write down how much it took and add that amount every day. After some period of time, the ammonia will drop to zero and the nitrites will rise. Once you have nitrites, cut your daily dose in half and continue to add it. The nitrites will spike off the charts. Eventually the nitrites will drop to zero and you'll have tons of nitrates. Do as many water changes as needed to drop the nitrate level to something reasonable (i shoot for under 20ppm but it can be a little higher), and then add the fish.
In addition to adding the ammonia, i also add a little fish food at several points in the cycle, say once a week. That ensures that the bacteria which convert organic wastes to ammonia are in your tank and hard at work before you add the fish, which directly release ammonia through the gills, but also release organic waste (poop) which is converted to ammonia and is then converted to nitrite, and finally to nitrate.
How long this all takes is hard to guess, there are a lot of variables, but i've had the cycle establish as quickly as 10 days, although i've also had it take 4 weeks, and 6 weeks is not unheard of. The benefit is that your bacterial colonies would be very well established and the fish would not come into prolonged contact with toxic levels of ammonia and nitrite. I have fully stocked my tank with this method several times and never saw measureable ammonia or nitrite, and no initial losses of even fairly sensitive species like the cardinals i have now.
Since you are cycling with fish, you need to minimize the fish's exposure to ammonia and nitrite by doing lots of water changes to keep those levels present but low, until the bacteria catch up to the bioload. Any materials from an established tank (like gravel, decorations, or filter media) that you can get your hands on can help shorten the time it takes to establish a new tank, when doing fishless or with fish cycling.
