I've read in a few places here that they don't care about your discharge, only whether or not you made it through nuke school. I guess that part only applies if you were a nuke, though.
As far as hiring practices, this may be true, but the question was about a security clearance. Since the discharge was due to a crime being committed, this may be quite different.
I received a bad conduct discharge 20 years ago and have not been in trouble since. The BCD was for larceny. Is there a chance I could get a security clearence? The larceny was for $100 and there was circumstances that allowed even though I was guilty I only served 5 months but ended up with only 3 months due to good behavior.
The best advice I can give is to take a stab at it. Be honest and answer all the questions to the best of your ability. Give all the information necessary to explain the circumstances. Twenty years is a long time and there are many people in nuclear power that have some offenses in their background at some point. The sad fact is that your chances may hinge on whether or not the background investigator is having a good day or a bad one (or has something similar in his/her own background.) If you have no other problems in the twenty ensuing years, you may have a good chance. If you don't try, you have no chance.
