Can a parent who regularly drinks /abuses alcohol get custody or visitation?
Yes, but in any custody or visitation order, the judge can require either or both parents (or any other person seeking custody or visitation) to not drink any alcohol. The judge can even require the parent to wear a continuous alcohol monitoring system1 (a device worn at all times that tests for alcohol levels through the skin)2 to make sure that this part of the custody/visitation order is being followed. The provider of the monitoring system would then be ordered by the judge to report any violation of the order to the court and to each party; and the parent can be held in contempt of court if s/he is found to have consumed alcohol.1
1 NCGS § 50-13.2(b2)
2 An example of a continuous alcohol monitoring system can be found here, although this is not necessarily the one that may be ordered by the judge in your case