Mine don't involve drugs. In fact, I've never even had a single toke in my life. All I am interested in is going to Nashville to see a songwriter friend of mine, and make it to a few motocross and NASCAR races. Oh, and I want to ride the dragon of course.
Well I don't know about your case but with me, I wasn't convicted (lawyer cut a deal!) and I had applied and received confirmation that arrest record was destroyed.
That being said I assume that when the US CBP hit the CPIC database, both when I crossed last year and when I applied for my Nexus card, the results were clean.