How likely is it that a student who has a 1.9 GPA and has appealed dismissal will be able to stay at CSU?
This is a complex question. First, you are already on Probation 2nd semester. If you are making progress toward getting off probation and you have few enough credits that taking another semester could put you over 2.0, then it is possible. Your chances also depend on how well written your appeal is.
Note that even after dismissal, you can take courses as a guest student (up to 6 credits at a time) to try to improve your GPA.