I'm an ACOA. Here's my personal perspective.
If you believe in people being empaths, do you think a child gets that from their parents?
I do believe some people are more empathetic than others (I am one of them). I feel other people's feelings. It's horrible. It's as though I have no skin. I don't think it is a heritable trait, but I do think that some people are just more sensitive to things. I don't believe it is something you LEARN; I believe it is something you ARE. For instance, sounds weird, but I have many times in life been able to SENSE when someone I have been close to is in trouble or in distress, without having been in any type of contact with them. It has happened too often for me to believe it was ever just sheer coincidence.
If so, do you think my son is reacting the way he does because he knows his mom is "off"?
Maybe. Maybe not. But not necessarily. What you describe about your son at that age I also witnessed in my niece with her mother. It may be just that these children crave or need more attention and love from their parent than that parent is able to give them. I personally think that when a small child like that wants picked up, the adult should pick the child up and comfort the child for whatever reason the child needs comfort. Unfortunately, alcoholic parents are rather selfish, and often put THEIR wants and needs before their childrens' wants and needs. Sadly, a mother's love cannot be replaced, IMO.
Ultimately, is this why, as others have stated, a child will eventually see through the BS of the drunk parent?
I don't think your scenario answers why the child will eventually see through the "BS" of the drunk parent. It is very difficult, as a child, to see through a drunk parent's BS. As a child, I did not have the analytical ability or even enough attention span to be able to begin to identify the alcoholic BS, nor did I ever even think to. Life was what it was; I was just learning my place in the world. I believe the effect of having an alcoholic parent was that I learned a sick, distorted view of my self, the world, and my place in it.
The only way I understood my father's "BS" was through what my mother said and how my mother acted in response to him, really. As an ACOA, I can tell you that EVERY word, every look, every gesture, every action that my father made toward me, I took 110% seriously. I did not begin to "see through the BS" until I was about 39 years old and that was some time after I had found Al-Anon. It is very difficult to be a child of an alcoholic, no matter what age. We are different. I have no doubt. IMO, the best thing you can do for your child is learn about children of alcoholics and do your best to teach him things that counterbalance what the alcoholic parent instills him. Like love, boundaries, forgiveness, peace, routine, etc. The same kinds of things we talk about on SR.
They learn that the sober parent is good and the drunk one is bad? Even at a young age?
In my experience, no. I loved and love BOTH my parents, I never saw my alcoholic parent as “bad.” I saw him as my dad. I think the way my mother talked about him, both then and now, and reacted to him, made it easier for me to, later in life, accept his alcoholism and deal with him in a healthy manner. My siblings, not so much. Your spouse is what she is. Life is what it is. We don't have to judge; it's counter-productive anyway. We can just accept. Hope something here is helpful to you.