I'd Love to tell you its possible, but as mentioned earlier, you would need to figure out your cost of living, how much or how little money you can live with, and inevitably, whether you were willing to make the sacrifices to "Live the Life".
I have seen a few take the risk and open up a shop of their own on some beach, somewhere. But a vast majority live in the ocean communities around the states and with cost of living and whatever other expenses you might have, teaching solely really isn't an option for most of us. I tried and quickly realized I couldn't live on what I earned solely from teaching.
Another problem to consider is how to continually bring in students...most dive shops have walk-ins, but they are split between the various instructors hurting for money. Some months people just aren't interested in getting into the water...especially if its cold outside...so you'll definately have slow times where money isn't coming in.
Teaching on your own also causes a problem as you will need to make arrangements for a pool to teach from. Most of us don't have a pool readily available and if you have a community pool from your condo complex or apt complex...they don't tend to like scuba in their pools for fear of damage.
One last thing to consider is I was teaching just about every day for a few months in a row at one point and I was just tired of getting into the water. Even Diving can be a bare if in excess.
I hope you the best and go after your dream if you can make it happen. I wish you the best. In the meantime, I'll stick to teaching part time when I retire.