Your son will benefit far more from a mom who lives a happy life solo than from a mom who lives an unhappy life with an alcoholic who is not in any kind of recovery. Don't get back together for your son. Do it for YOU. There are other ways to have male influence in his life. You want GOOD male influence, not a dry (or not) drunk.
Your 12 year old will transition into teen years and see things much differently as he goes through various phases of growing. What he sees now as his dad figure may change. I have seen this with my own kids ages 18, 17, 14 and 11. The 11 year old still idolizes my AH, but the older ones are seeing him in a far different light now that they are in their teen years. His alcoholic behavior has been truly damaging to them, even when he's sober.