A good friend of mine is a felon and a union master electrician. He makes a decent living, when there's work, and his past doesn't seem to make a difference to his employers. There are definitely many paths one can take; code is a really good one, let's be honest, but it's not the only one.
I believe this is a possibility that is dependent on state licensing laws. In some states, the licensing body may not automatically disqualify felons. In other states, they make exceptions on a case-by-case basis. And in the third category, it is automatically disqualifying. Something to definitely look into, though.