lksdrinker touched the more important aspects. A drop checker is a cheap way to double check your CO2 distribution and conc. It also acts as a visual warning in case something went wrong with your CO2 setup... timer got bust, solenoid stuck, CO2 tank empty, etc. Unlike, KH/pH CO2 conc. calculations a drop checker is not influenced by things dissolved in water (except CO2). For most KH/pH works, but there are aquariums where the results of alkalinity is not a good approximate of KH.
If you use a liquid pH test or one of the pH pens, you also sample the top layer of water... what about that bottom corner where the HC doesn't grow ? A drop checker can give a general idea of what is happening there. BTW a drop checker tells you nothing about the exact aquarium pH unless you have a KH of 4. Fish tolerance varies and fish can adjust in time to higher CO2 conc. But it is good practice to observe the fish behavior. If they gasp at the surface you might need to increase water surface agitation. If they stay at the bottom, kind of drunk , bouncing from one side to the other reduce the CO2.
Can you run your setup without it, sure just as you can without a pH test. They are both just tools that aid in achieving your purpose if you understand and apply correctly. I would add it to the list of things I would buy ...
On hiatus till later this year