i'm not a law expert, but i would think it depends on the types of felonies on your name.
the first thing they're going to do when you want to be a teacher is they're going to check your criminal history... depending on what the felonies are you might be able to make it, but maybe not.
With felonies your chances of becoming a teacher are almost zero.
You might be able to get some kind of a job in a school, but with regulations getting tighter on who is hired to be around children, those chances are really small too.
The question is can you get a job. First thing they do is a background check...
I doubt it.