Diagnosis and definition of mental illness aside, how is your friend being treated for his ADHD? Carrying a firearm while under the influence of a controlled substance is a big no-no, and it's my guess that he is being treated with Adderall/Ritalin/Concerta/etc. (which are all Schedule 2 drugs, read: controlled substance)?
Currently no treatment.
Good, one less thing to worry about at the moment. Any idea if he will be seeking active treatment?
Typical first-line treatment for ADHD will be your C-2 stimulants, however there are other alternatives that are non-controlled substances. As far as I know, Strattera is the only FDA-indicated medication for treatment of ADHD, though there are other medications with off-label use (Bupropion, clonidine, and the TCAs [amitriptyline, desipramine, imipramine]). If he chooses to proceed with his CPL application and finds himself seeking treatment, his physician should be able to address the issue of using a medication that is not a controlled substance and is suited for him.