Just in my experience stated above. Being a sober addict, and working with addicts. That's not what it sounded like to me. Usually the first few weeks would be when that would be super noticable.
Following that for the next year or so depending on the drug you will be in PAWS (post acute withdrawal syndrome). Which will have some effects on mood, and even some physical effects like temporarily being uncoordinated at times.
What I saw with him wasn't someone in early sobriety. It was someone that was messed up. I've seen people that were literally on deaths door come in and get sober. And it's a very noticeable change within a month. You generally won't see someone get sober. Start acting sober, then suddenly they seem exactly like they did when they are using. Unless they are using.