This is a question we see time and again written by beginners and on "low tech" Face Book Pages. Is it possible to grow some plants without supplemental CO2? Of course it is. It is a matter of balancing the amount of light you put over the system and the amount of nutrients provided. Too much light without adding CO2 will give you HUGE algae problems with little added growth. It just so happens that I got some really extraordinary photos of one of my tanks many years ago when I was beta testing some products for a company, and they wanted me to first grow the tank without supplemental CO2. Here is the tank. Not horrible... Some people would be satisfied with this, even today.
When the test period was over, I didn't have a regulator or CO2 tank sitting around. But I did have two small commercial yeast reactors made by Hagen sitting around, that I had won at a club auction. This was a 75 gallon tank, and those yeast reactors seemed woefully undersized, but I figured some CO2 was better than none and I stuck them on the tank. Here is the result only a few weeks later. This was the ONLY change I made to the tank. If you study the photos carefully, you can see the same plants in the same positions. They are just much more robust. I can't emphasize enough how important supplemental CO2 is on a planted tank, even if it is just a simple yeast reactor.
Likewise, I happened, after the fact, to find that I had two photos of a different 75 gallon tank in a very nutrient poor condition, and then with better fertilization. I had a pair of Farlowella catfish that kept spawning right near the top of the tank. (you can see one of them guarding the eggs in the upper right hand corner of the tank) Since they were spawning right at the top, I could only change a few inches of water at a time. Because of that, I was reluctant to add too much fertilizer. Things happen slowly in a tank, and I didn't even realize how the plants were stunting.
The female Farlowella died, putting an end to the breeding project. At that point, I did a large water change and started fertilizing as I normally would again. Below you will see another photo of the tank after a few weeks of proper fertilization.
Again, although these are old photos, if you click on the photos to enlarge them, you will find the same plants in the same places in the tank. The only change is that the tank was now being adequately fed.
I hope these photos help convince you of the benefits of supplemental CO2 and good fertilization!