I can't speak for any specific facility. But, it is possible. There are a few people I know of personally who were convicted of felonies who have since gotten unescorted access.
I think the most important information is that they are not related to drug use or trafficking, and that they are not related to any activity that could be considered terrorism or attempts to subvert or overthrow the lawfully instituted government.
Being 18 at the time of the offense takes away the youthful offender status, but the fact that the subject has reached a more mature age with no infractions in 7 years does indicate that the crimes may have been partly attributable to the immaturity of the subject at a young age, and that he is rehabilitated.
But the proof of the pudding, as they say, is in the eating. You will never know the answer to this question unless or until he applies for access. The very worst thing that can happen is that they say "no". Of course, there may be some travel and expense involved in going to a site and waiting a week or more for the answer. This is usually the reason why people don't try when they are not sure. The money you spend for travel, meals, and lodging at a site away from home can be seen as a gamble if you don't think you're going to get in - especially since a lot of companies won't pay for any of that, and those who will pay for it won't pay if you don't get the badge. So, the best way to get the answer to this question is to apply somewhere and be prepared to eat the cost. There are certainly ways to minimize that.
