Can you legally be recognized as being married by common law if your spouse will not answer the door to be served with the divorce notice which was filed in September in the state of NJ?

It is unclear why you wonder about being married under common law in the same sentence you speak of serving divorce papers.

1.) There is no common law marriage in New Jersey.

2.) Failure to answer the door has no effect on the marriage or legal relationship between the parties.

3.) A person cannot stop a divorce by not answering the door.

4.) You need to consult with an attorney who specializes in divorce.