Maybe I can offer a kids persepective on this. I didn't "meet" my father until I was 7 years old. It was weird seeing and speaking to him. We didn't know each other at all and had no idea what our relationship was supposed to be like. But I was very happy to have my Dad in mylife. It was always something I was missing. Remember you are the adult and it is your job to try and find things you can do together but beleive me just the fact that you are around now means the world to your little boy. My Dad began sending me cards in the mail for every little holiday and sometimes just "thinking of you" cards in between. That made me feel connected to him just cuz it showed he was thinking of me. If you could do that Im sure your son will appreciate it. Just a card that costs a buck and a stamp to mail it would be good.
My story ended with father actually committing suicide about 3 years after we met. He had problems and addictions as well. I can say that was the most hurtful thing ever cuz I felt I was cheated out of a relationship with him, as awkward as things may have been when he was alive. Please get that thought out of your head bacause it is a very selfish thing to do and absolutly would have a negative impact on him.