Yes it is possible to have the Brazilian done after you have previously chemically straightened your hair. It will make the hair soft and shiny and almost back to perfect health.
The only thing is that if you have very curly hair, and you do not want to use the chemical straightener anymore, you will not get the same straight results from only doing the Brazilian. The Brazilian is a TREATMENT that has the ability to take away FRIZZ. It does not make the hair too straight.
My advice is to carry on doing your roots with the chemical straightener, and every 3-4 months do the Brazilian over it.