It's certainly possible but not that easy because much depends on a teacher's marketing ability. The single biggest problem is cancellations. Thais are the 'let's cancel a lesson at the last minute' world champions. Many freelance teachers give up for this reason alone and seek the security of a job with a guaranteed income. Ajarn.com also has a more in-depth article on 'freelance teaching' that might interest you.
Ian says "I used to teach quite a few private students. If you think of your privates as the icing on the cake ( I could have phrased that better but I'm sure you get the drift) then you'll be OK. I'm pretty laid back so as long as mine give me 24 hours notice then I've got no problem if they cancel. It's nice to have an evening free sometimes"