Does alcohol slow down post-surgical recovery?

Yes. In moderation probably not. Alcohol in combination with the pain pills given to you by your surgeon could cause harm. Also alcohol is "empty" calories, and you need good nutrition, especially protein, to heal.
It can. Alcohol causes the cells that produce clotting to not work as well and can even reduce their number; it also reduces activity of cells that lay down scar. Smoking cigarettes has even more effects, and when people who are drinking also smoke, the effects are multiplied. This is especially true in orthopedic surgeries, especially spine surgery. Alcohol also increases risk of infection.